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Title | : On the freeness of anticyclotomic Selmer groups of modular forms |
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Author | : Chan-Ho Kim, Robert Pollack, Tom Weston |
Journal | : International Journal of Number Theory, accepted |
NUMBER | M16004 |
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AUTHOR | Chan-Ho Kim, Robert Pollack, Tom Weston |
TITLE | On the freeness of anticyclotomic Selmer groups of modular forms |
ARCHIVE | |
FILE | freeness_IJNT_submit.pdf |
JOURNAL | International Journal of Number Theory, accepted |
ABSTRACT | We establish the freeness of certain anticyclotomic Selmer groups of modular forms. The freeness of these Selmer groups plays a key role in the Euler system arguments introduced in [BD05]. In particular, our result fills some implicit gaps in [PW11] and [CH15] which in turn allows the results of these papers to hold for modular forms whose residual representations are not minimally ramified. Removing these minimal ramification conditions is essential for applications of congruences of modular forms to anticyclotomic Iwasawa theory as in [PW11, ¡×7] and [Kim]. |
Title | : Anticyclotomic Iwasawa invariants and congruences of modular forms |
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Author | : Chan-Ho Kim |
Journal | : Asian Journal of Mathematics, to appear |
NUMBER | M15013 |
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AUTHOR | Chan-Ho Kim |
TITLE | Anticyclotomic Iwasawa invariants and congruences of modular forms |
ARCHIVE | |
FILE | summary_revised_final.pdf |
JOURNAL | Asian Journal of Mathematics, to appear |
ABSTRACT | The main purpose of this article is to examine how congruences between Hecke eigensystems of modular forms affect the Iwasawa invariants of their anticyclotomic p-adic L-functions. We apply Greenberg- Vatsal and Emerton-Pollack-Westons ideas on the variation of Iwasawa invariants under congruences to the anticyclotomic setting. As an application, we establish infinitely many new examples of the anticyclotomic main conjecture for modular forms, which cannot be treated by Skinner-Urbans work. An explicit example is given. |
Title | : Circle actions on almost complex manifolds with isolated fixed points |
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Author | : Donghoon Jang |
Journal | : |
NUMBER | M15010 |
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AUTHOR | Donghoon Jang |
TITLE | Circle actions on almost complex manifolds with isolated fixed points |
ARCHIVE | arXiv:1510.00952 |
FILE | 1510.00952.pdf |
JOURNAL | |
ABSTRACT | The author proved that if the circle acts symplectically on a compact, connected symplectic manifold M with three fixed points, then M is equivariantly symplectomorphic to some standard action on $mathbb{CP}^2$. In this paper, we extend the result to a circle action on an almost complex manifold; if the circle acts on a compact, connected almost complex manifold M with exactly three fixed points, then $dim M=4$. Moreover, we deal with the cases of one fixed point and two fixed points. |
Title | : Non-Kahler complex structures on R^4 II |
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Author | : Di Scala Antonio J., Kasuya Naohiko, Zuddas Daniele |
Journal | : |
NUMBER | M16005 |
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AUTHOR | Di Scala Antonio J., Kasuya Naohiko, Zuddas Daniele |
TITLE | Non-Kahler complex structures on R^4 II |
ARCHIVE | 1511.08471 |
FILE | Non-Kahler-II.pdf |
JOURNAL | |
ABSTRACT | We follow our study of non-Kahler complex structures on R^4 that we defined in a previous paper. We prove that these complex surfaces do not admit any smooth complex compactification. Moreover, we give an explicit description of their meromorphic functions. We also prove that the Picard groups of these complex surfaces are uncountable, and give an explicit description of the canonical bundle. Finally, we show that any connected non-compact oriented 4-manifold admits complex structures without Kahler metrics. |
Title | : On branched covering representation of 4-manifolds |
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Author | : Piergallini Riccardo, Zuddas Daniele |
Journal | : |
NUMBER | M16003 |
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AUTHOR | Piergallini Riccardo, Zuddas Daniele |
TITLE | On branched covering representation of 4-manifolds |
ARCHIVE | 1602.07459 |
FILE | BC4-manifolds.pdf |
JOURNAL | |
ABSTRACT | We provide new branched covering representations for bounded and/or non-compact 4- manifolds, which extend the known ones for closed 4-manifolds. Assuming M to be a connected oriented PL 4-manifold, our main results are the following: (1) if M is compact with (possibly empty) boundary, then it is a simple branched cover of S^4 minus some 4-balls; (2) if M is open, then it is a simple branched cover of S^4 minus the end space of M, which is tamely embedded in S^4. We also define the notion of branched covering between topological manifolds, which extends the usual one in the PL category. In this setting, as an interesting consequence of the above results, we prove that any closed oriented topological 4-manifold is a 4-fold branched covering of S^4. According to almost-smoothability of 4-manifolds, this branched cover could be wild at a single point. |
Title | : Non-Kahler complex structures on R^4 |
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Author | : Di Scala Antonio J., Kasuya Naohiko, Zuddas Daniele |
Journal | : Geometry & Topology |
NUMBER | M15001 |
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AUTHOR | Di Scala Antonio J., Kasuya Naohiko, Zuddas Daniele |
TITLE | Non-Kahler complex structures on R^4 |
ARCHIVE | 1501.06097 |
FILE | Non-Kahler-R4.pdf |
JOURNAL | Geometry & Topology |
ABSTRACT | We construct the first examples of non-Kahler complex structures on R^4. These complex surfaces have some analogies with the complex structures constructed in early Fifties by Calabi and Eckmann on the products of two odd-dimensional spheres. However, our construction is quite different from that of Calabi and Eckmann. |
Title | : On embeddings of almost complex manifolds in almost complex Euclidean spaces |
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Author | : Di Scala Antonio J., Kasuya Naohiko, Zuddas Daniele |
Journal | : Journal of Geometry and Physics 101 (2016) 19-26 |
NUMBER | M14015 |
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AUTHOR | Di Scala Antonio J., Kasuya Naohiko, Zuddas Daniele |
TITLE | On embeddings of almost complex manifolds in almost complex Euclidean spaces |
ARCHIVE | 1410.1321 |
FILE | embeddings.pdf |
JOURNAL | Journal of Geometry and Physics 101 (2016) 19-26 |
ABSTRACT | We prove that any compact almost complex manifold (M, J) of real dimension 2m admits a pseudo-holomorphic embedding in a Euclidean space of dimension 4m + 2, endowed with a suitable non-standard almost complex structure. Moreover, we give a necessary and sufficient condition, expressed in terms of the Segre class of (M, J), for the existence of an embedding or an immersion in an almost complex Euclidean 4m-space. We also discuss the pseudo-holomorphic embeddings of an almost complex 4-manifold in R^6. |
Title | : Universal Lefschetz fibrations and Lefschetz cobordisms |
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Author | : Zuddas, Daniele |
Journal | : Geometry & Topology Monographs 19 (2015) 125-144 |
NUMBER | M14009 |
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AUTHOR | Zuddas, Daniele |
TITLE | Universal Lefschetz fibrations and Lefschetz cobordisms |
ARCHIVE | 1403.2203 |
FILE | universalfib2.pdf |
JOURNAL | Geometry & Topology Monographs 19 (2015) 125-144 |
ABSTRACT | We construct universal Lefschetz fibrations, that are defined in analogy with the classical universal bundles. We also introduce the cobordism groups of Lefschetz fibrations, and we see how these groups are quotient of the singular bordism groups via the universal Lefschetz fibrations. |
Title | : Lefschetz fibrations over the disc |
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Author | : Apostolakis Nikos, Piergallini Riccardo, Zuddas Daniele |
Journal | : Proceedings of the London Mathematical Society 107 (2013) 340-390 |
NUMBER | M14007 |
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AUTHOR | Apostolakis Nikos, Piergallini Riccardo, Zuddas Daniele |
TITLE | Lefschetz fibrations over the disc |
ARCHIVE | 1104.4536 |
FILE | |
JOURNAL | Proceedings of the London Mathematical Society 107 (2013) 340-390 |
ABSTRACT | We provide a complete set of moves relating any two Lefschetz fibrations over the disc having as their total space the same four-dimensional 2-handlebody up to 2-equivalence. As a consequence, we also obtain moves relating diffeomorphic three-dimensional open books, providing a different approach to an analogous previous result by Harer. |
Title | : Universal Lefschetz fibrations over bounded surfaces |
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Author | : Zuddas Daniele |
Journal | : Algebraic & Geometric Topology 12 (2012) 1811-1829 |
NUMBER | M14006 |
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AUTHOR | Zuddas Daniele |
TITLE | Universal Lefschetz fibrations over bounded surfaces |
ARCHIVE | 1106.3530 |
FILE | Universal1.pdf |
JOURNAL | Algebraic & Geometric Topology 12 (2012) 1811-1829 |
ABSTRACT | In analogy with the vector bundle theory we define universal and strongly universal Lefschetz fibrations over bounded surfaces. After giving a characterization of these fibrations we construct very special strongly universal Lefschetz fibrations when the fiber is the torus or an orientable surface with connected boundary and the base surface is the disk. As a by-product we also get some immersion results for 4-dimensional 2- handlebodies. |
Title | : Embedding almost-complex manifolds in almost-complex euclidean spaces |
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Author | : Di Scala Antonio J, Zuddas Daniele |
Journal | : Journal of Geometry and Physics |
NUMBER | M14005 |
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AUTHOR | Di Scala Antonio J, Zuddas Daniele |
TITLE | Embedding almost-complex manifolds in almost-complex euclidean spaces |
ARCHIVE | 1005.4619 |
FILE | embedding1.pdf |
JOURNAL | Journal of Geometry and Physics |
ABSTRACT | We show that any compact almost-complex manifold (M, J) of complex dimension m can be pseudo-holomorphically embedded in R^{6m} equipped with a suitable almost- complex structure. |
Title | : Representing Dehn twists with branched coverings |
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Author | : Zuddas Daniele |
Journal | : Int. Math. Res. Notices |
NUMBER | M14004 |
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AUTHOR | Zuddas Daniele |
TITLE | Representing Dehn twists with branched coverings |
ARCHIVE | 0710.0102 |
FILE | dehn.pdf |
JOURNAL | Int. Math. Res. Notices |
ABSTRACT | We show that any homologically nontrivial Dehn twist of a compact surface F with boundary is the lifting of a half-twist in the braid group B_n, with respect to a suitable branched covering p : F --> B^2. In particular, we allow the surface to have disconnected boundary. As a consequence, any allowable Lefschetz fibration on B^2 is a branched covering of B^2 x B^2. |
Title | : A universal ribbon surface in B^4 |
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Author | : Piergallini Riccardo, Zuddas Daniele |
Journal | : Proc. London Math. Soc. |
NUMBER | M14003 |
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AUTHOR | Piergallini Riccardo, Zuddas Daniele |
TITLE | A universal ribbon surface in B^4 |
ARCHIVE | math/0308222 |
FILE | universal_surface.pdf |
JOURNAL | Proc. London Math. Soc. |
ABSTRACT | We construct an orientable ribbon surface F in B^4, which is universal in the following sense: any compact orientable pl 4-manifold having a handle decomposition with 0-, 1- and 2-handles can be represented as a cover of B^4 branched over F. |
Title | : Braiding non-orientable surfaces in S^4 |
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Author | : Piergallini Riccardo, Zuddas Daniele |
Journal | : Atti Sem. Mat. Fis. Univ. Modena |
NUMBER | M14002 |
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AUTHOR | Piergallini Riccardo, Zuddas Daniele |
TITLE | Braiding non-orientable surfaces in S^4 |
ARCHIVE | |
FILE | braiding.pdf |
JOURNAL | Atti Sem. Mat. Fis. Univ. Modena |
ABSTRACT | Closed braided surfaces in S^4 are the two-dimensional analogous of closed braids in S^3. They are useful in studying smooth closed orientable surfaces in S^4, since any such a surface is isotopic to a braided one. We show that the non-orientable version of this result does not hold, that is smooth closed non-orientable surfaces cannot be braided. In fact, any reasonable definition of non-orientable braided surfaces leads to very strong restrictions in terms of selfintersection and Euler characteristic. |
Title | : Some remarks on Bergmann metrics |
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Author | : Loi Andrea, Zuddas Daniele |
Journal | : Riv. Mat. Univ. Parma |
NUMBER | M14001 |
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AUTHOR | Loi Andrea, Zuddas Daniele |
TITLE | Some remarks on Bergmann metrics |
ARCHIVE | |
FILE | bergmann.pdf |
JOURNAL | Riv. Mat. Univ. Parma |
ABSTRACT | In this paper we study the set of self-Bergmann metrics on the Riemann sphere endowed with the Fubini-Study metric and we extend a theorem of Tian to the case of the punctured plane endowed with a natural flat metric. |
Title | : Geometric structures modeled on smooth projective horospherical varieties of Picard number one |
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Author | : ±è½Å¿µ |
Journal | : |
NUMBER | M16006 |
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AUTHOR | ±è½Å¿µ |
TITLE | Geometric structures modeled on smooth projective horospherical varieties of Picard number one |
ARCHIVE | arXiv:1610.01275 |
FILE | |
JOURNAL | |
ABSTRACT | Geometric structures modeled on rational homogeneous manifolds are studied to characterize rational homogeneous manifolds and to prove their deformation rigidity. To generalize these characterizations and deformation rigidity results to quasihomogeneous varieties, we first study horospherical varieties and geometric structures modeled on horospherical varieties. Using Cartan geometry, we prove that a geometric structure modeled on a smooth projective horospherical variety of Picard number one is locally equivalent to the standard geometric structure when the geometric structure is defined on a Fano manifold of Picard number one. |