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Non-isomorphic abelian varieties with the same arithmetic [PDF]
Royal Society Open ScienceWe construct two abelian varieties over [Formula: see text] which are not isomorphic, but have isomorphic Mordell–Weil groups over every number field, isomorphic Tate modules and equal values for several other invariants.
Jamie Bell
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Abelian varieties with isogenous reductions [PDF]
Comptes Rendus. Mathématique, 2021 Let $A_1$ and $A_2$ be abelian varieties over a number field $K$. We prove that if there exists a non-trivial morphism of abelian varieties between reductions of $A_1$ and $A_2$ at a sufficiently high percentage of primes, then there exists a non-trivial
Khare, Chandrashekhar B. +1 more
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On the minimal model program for projective varieties with pseudo-effective tangent sheaf [PDF]
Épijournal de Géométrie Algébrique, 2023 In this paper, we develop a theory of pseudo-effective sheaves on normal projective varieties. As an application, by running the minimal model program, we show that projective klt varieties with pseudo-effective tangent sheaf can be decomposed into Fano ...
Shin-ichi Matsumura
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Abelian varieties over fields of finite characteristic
Open Mathematics, 2014 Zarhin Yuri
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Angehrn-Siu-Helmke’s method applied to abelian varieties
Forum of Mathematics, Sigma, 2023 We apply Angehrn-Siu-Helmke’s method to estimate basepoint freeness thresholds of higher dimensional polarized abelian varieties. We showed that a conjecture of Caucci holds for very general polarized abelian varieties in the moduli spaces $\mathcal {
Zhi Jiang
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Non-linear bi-algebraic curves and surfaces in moduli spaces of Abelian differentials
Comptes Rendus. Mathématique, 2023 The strata of the moduli spaces of Abelian differentials are non-homogenous spaces carrying natural bi-algebraic structures. Partly inspired by the case of homogenous spaces carrying bi-algebraic structures (such as torii, Abelian varieties and Shimura ...
Deroin, Bertrand, Matheus, Carlos
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Free dihedral actions on abelian varieties
Cubo, 2021 We give a simple construction for hyperelliptic varieties, defined as the quotient of a complex torus by the action of a finite group $G$ that contains no translations and acts freely, with $G$ any dihedral group. This generalizes a construction given by
Bruno Aguiló Vidal
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Characterization of abelian varieties [PDF]
Inventiones Mathematicae, 2001 10 pages ...
Chen, J.A., Hacon, C.D.
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Logarithmic Abelian Varieties [PDF]
Nagoya Mathematical Journal, 2008 AbstractWe develop the algebraic theory of log abelian varieties. This is Part II of our series of papers on log abelian varieties, and is an algebraic counterpart of the previous Part I ([6]), where we developed the analytic theory of log abelian varieties.
Kajiwara, Takeshi +2 more
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Compact connected components in relative character varieties of punctured spheres [PDF]
Épijournal de Géométrie Algébrique, 2021 We prove that some relative character varieties of the fundamental group of a punctured sphere into the Hermitian Lie groups $\mathrm{SU}(p,q)$ admit compact connected components.
Nicolas Tholozan, Jérémy Toulisse
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