相关论文: Formal Brauer groups and the moduli of abelian sur…

We introduce a stratification on the space of symplectic flags on the de Rham bundle of the universal principally polarized abelian variety in positive characteristic and study its geometric properties like irreducibility of the strata and…

We show that the (compactified) moduli space of abelian surfaces with a polarisation of type $(1,p^2)$ is of general type for $p \ge 11$, improving a result of O'Grady.

The toroidal compactification of the moduli space of complex abelian surfaces with a polarisation of type (1,p), p a prime, is of general type if p is at least 173. Happy Christmas.

We construct a compactification of the moduli spaces of abelian differentials on Riemann surfaces with prescribed zeroes and poles. This compactification, called the moduli space of multi-scale differentials, is a complex orbifold with…

Let $S$ be an abelian surface over an algebraically closed field $k$ with characteristic different from $2$ and $3$, and $\mathcal{L}$ a symmetric ample line bundle defining a polarisation of type $(1,3)$. Then the linear system…

In this paper a number of results on cycles on the moduli space of principally polarized abelian varieties is presented. Results include a determination of the tautological ring, bounds on the order of torsion of the top Chern class…

We study the birational geometry of some moduli spaces of abelian varieties with extra structure: in particular, with a symmetric theta structure and an odd theta characteristic. For a $(d_1,d_2)$-polarized abelian surface, we show how the…

The moduli space of principally polarized abelian varieties with real structure and with level $N=4m$ structure (with $m \ge 1$) is shown to coincide with the set of real points of a quasi-projective algebraic variety defined over $\mathbb…

For $4 \nmid L$ and $g$ large, we calculate the integral Picard groups of the moduli spaces of curves and principally polarized abelian varieties with level $L$ structures. In particular, we determine the divisibility properties of the…

Compactifications of moduli spaces of (1,p)-polarized abelian surfaces with level structures of canonical type have been described in great detail by Hulek, Kahn and Weintraub. The aim of this paper is to determine some invariants of smooth…

We prove that the moduli space X(1,7) of (1,7)-polarized abelian surfaces with canonical level structure is birational to the Fano 3-fold V22 of polar hexagons of the Klein quartic X(7). In particular X(1,7) is rational and the birational…

The moduli space of abelian surfaces with polarisation of type (1,t) and a bilevel structure is of general type if t is odd and at least 17.

This is the sequel to arXiv:math/0001089. In this paper, we complete the promised description of moduli of abelian surfaces of low degree, covering the cases of degree (1,12), (1,14), (1,16), (1,18) and (1,20). In each case, we describe…

We compute explicit rational models for some Hilbert modular surfaces corresponding to square discriminants, by connecting them to moduli spaces of elliptic K3 surfaces. Since they parametrize decomposable principally polarized abelian…

We compute the $\ell$-primary torsion of the Brauer group of the moduli stack of smooth curves of genus three over any field of characteristic different from two and the Brauer group of the moduli stacks of smooth plane curves of degree $d$…

We compute the Brauer group of the moduli stack of stable PGL(r)-bundles on a curve $X$ over an algebraically closed field of characteristic zero. We also show that the Brauer group of such a moduli stack coincides with the Brauer group of…

We compute the Brauer group of the moduli stack of elliptic curves over the integers, localizations of the integers, finite fields of odd characteristic, and algebraically closed fields of characteristic not $2$. The methods involved…

Consider all moduli points corresponding with polarized abelian varieties in characteristic p such that the associated quasi-polarized p-divisible group is geometrically isomorphic with a given one. This defines a subset C of the moduli…

The moduli space of abelian surfaces with polarisation of type (1,6) and a bilevel structure has positive Kodaira dimension. By contrast, Mukai has shown that the moduli space of bilevel-t abelian sufaces is rational for t=2,3,4,5.

In this paper the authors consider a certain toroidal compactification of the moduli space of degenerations of (1,p)-polarized abelian surfaces with (canonical) level structure. Using Hodge theory we give a proof that a degenerate abelian…