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Cohomology of Moduli Space of Cubic Fourfolds I
In this paper we compute the cohomology of moduli space of cubic fourfolds with ADE type singularities relying on Kirwan’s blowup and Laza’s GIT...
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Abelian varieties with finite abelian group action
An automorphism of an abelian variety induces a decomposition of the variety up to isogeny. There are two such results, namely the isotypical...
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Metric distortion in the geometric Schottky problem
The classical Schottky problem is concerned with characterization of Jacobian varieties of compact Riemann surfaces among all abelian varieties, or...
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Serre’s tensor construction and moduli of abelian schemes
Given a polarized abelian scheme with action by a ring, and a projective finitely presented module over that ring, Serre’s tensor construction...
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Tropicalization of Classical Moduli Spaces
The image of the complement of a hyperplane arrangement under a monomial map can be tropicalized combinatorially using matroid theory. We apply this...
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Canonical key formula for projective abelian schemes
In this paper we prove a refined version of the canonical key formula for projective abelian schemes in the sense of Moret-Bailly (cf. Astérisque...
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Group schemes of period 2
We give an explicit construction of the antiequivalence of the category of finite flat commutative group schemes of period 2 defined over a valuation...
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Compactifications of universal abelian threefolds with CM
We determine completions of semi-abelian degenerations of abelian threefolds with complex multiplication. This type of completion plays a crucial...
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On automorphisms of principally polarized abelian varieties
Let ( X , H ) be a g -dimensional principally polarized abelian variety (p.p.a.v.) and Aut( X , H ) its group of automorphisms, in this brief survey we...
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Products of Jacobians as Prym-Tyurin varieties
Let X 1 , ..., X m denote smooth projective curves of genus g i ≥ 2 over an algebraically closed field of characteristic 0 and let n denote any...
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The loci of abelian varieties with points of high multiplicity on the theta divisor
We study the loci of principally polarized abelian varieties with points of high multiplicity on the theta divisor. Using the heat equation and...
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Uniform boundedness of level structures on abelian varieties over complex function fields
Let X = Ω/Γ be a smooth quotient of a bounded symmetric domain Ω by an arithmetic subgroup
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On the 0-dimensional irreducible components of the singular locus of \(\mathcal{A}_g\)
In this short note we give a characterization of extremal principally polarized abelian varieties determining an isolated point in Sing
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On two theorems for flat, affine group schemes over a discrete valuation ring
We include short and elementary proofs of two theorems that characterize reductive group schemes over a discrete valuation ring, in a slightly more...
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The Moduli Space of Real Abelian Varieties with Level Structure
The moduli space of principally polarized Abelian varieties with real structure and with level N = 4 m structure (with m ≥1) is shown to coincide with...
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The Moduli Space of (1,11)-Polarized Abelian Surfaces is Unirational
We prove that the moduli space A
11 lev of (1,11)-polarized Abelian surfaces with level structure of canonical type is birational to Klein's cubic... -
Calabi–Yau Threefolds and Moduli of Abelian Surfaces I
We describe birational models and decide the rationality/unirationality of moduli spaces A d (and A
d lev ) of (1, d )-polarized Abelian surfaces...