Results 11 to 20 of about 2,776 (226)
The Picard Group of the Universal Abelian Variety and the Franchetta Conjecture for Abelian Varieties [PDF]
Michigan Mathematical Journal, 2019 We compute the Picard group of the universal abelian variety over the moduli stack $\mathscr A_{g,n}$ of principally polarized abelian varieties over $\mathbb{C}$ with a symplectic principal level $n$-structure. We then prove that over $\mathbb{C}$ the statement of the Franchetta conjecture holds in a suitable form for $\mathscr A_{g,n}$.
Fringuelli R., Pirisi R.
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Degenerating abelian varieties via log abelian varieties [PDF]
This thesis is based on the author's paper [52]. It extends the construction of log Tate curves from [25, §1] to higher dimensions. The approach involves extensive applications of algebraic spaces and higher-dimensional convex geometry to create diverse models for any given split totally degenerate semi-stable abelian variety over a complete discrete ...
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Every finite abelian group is the group of rational points of an ordinary abelian variety over F2, F3 and F5 [PDF]
, 2023 We show that every finite abelian group occurs as the group of rational points of an ordinary abelian variety over F 2, F 3 and F 5. We produce partial results for abelian varieties over a general finite field F q.
Marseglia, Stefano, Springer, Caleb
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Degree of irrationality of a very general Abelian variety [PDF]
, 2022 Consider a very general abelian variety of dimension at least and an integer . We show that if the map has a -dimensional fiber then . This extends results of the second-named author which covered the cases .
O. Martin +7 more
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Invariant Brauer group of an abelian variety [PDF]
, 2021 We study a new object that can be attached to an abelian variety or a complex torus: the invariant Brauer group, as recently defined by Yang Cao. Over the field of complex numbers this is an elementary abelian 2-group with an explicit upper bound on the ...
Valloni, Domenico +9 more
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Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms [PDF]
, 2021 Assuming the Mumford–Tate conjecture, we show that the center of the endomorphism ring of an abelian variety defined over a number field can be recovered from an appropriate intersection of the fields obtained from its Frobenius endomorphisms.
Costa, Edgar +2 more
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Transposition Regular AG-Groupoids and Their Decomposition Theorems
Mathematics, 2022 In this paper, we introduce transposition regularity into AG-groupoids, and a variety of transposition regular AG-groupoids (L1/R1/LR, L2/R2/L3/R3-groupoids) are obtained. Their properties and structures are discussed by their decomposition theorems: (1)
Yudan Du, Xiaohong Zhang, Xiaogang An
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Nagoya Mathematical Journal, 1953 In a Bourbaki seminary note, La Théorie des Fonctions Thêta, A. Weil has discussed two fundamental theorems of the general theory of Theta functions. The first, due to H. Poincaré, was proved very skilfully in the note by means of harmonic integrals on a torus and the second, due to Frobenius, was treated by the systematic use of the notion of analytic
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Calabi–Yau threefolds and moduli of abelian surfaces I [PDF]
, 2001 We describe birational models and decide the rationality/unirationality of moduli spaces $\cal A$d (and $\cal A$levd) of (1, d)-polarized Abelian surfaces (with canonical level structure, respectively) for small values of d.
Sorin Popescu +3 more
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Many phases of generalized 3D instanton crystals
SciPost Physics, 2021 Nuclear matter at large number of colors is necessarily in a solid phase. In particular holographic nuclear matter takes the form of a crystal of instantons of the flavor group. In this article we initiate the analysis of the three-dimensional crystal
Matti Jarvinen, Vadim Kaplunovsky, Jacob Sonnenschein
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