Related papers: Singularities in the Ekedahl--Oort stratification

In this expository note, recent results of Kishimoto and Matsushita on triangulated manifolds are linked to the classical criterion on the normal Stiefel-Whitney classes for existence of an embedding of a smooth closed manifold into…

We give an explicit formula for the Mordell-Weil rank of an abelian fibered variety and some of its applications for an abelian fibered hyperk\"ahler manifold. As a byproduct, we also give an explicit example of an abelian fibered variety…

We study the Ekedahl-Oort stratification on moduli spaces of PEL type. The strata are indexed by cosets in a Weyl group. The main result of this paper is that the dimension of a stratum equals the length of the corresponding Weyl group…

This paper is a contribution to the general problem of giving an explicit description of the basic locus in the reduction modulo $p$ of Shimura varieties. Motivated by \cite{Vollaard-Wedhorn} and \cite{Rapoport-Terstiege-Wilson}, we…

In this paper we investigate the orbit closures for the class of representations of simple algebraic groups associated to various gradings on a simple Lie algebras of type $E_6$, $F_4$ and $G_2$. The methods for classifying the orbits for…

For g>2 we study the cohomology classes in the closure of a stratum of abelian differentials defined by the boundary strata of codimension one. As an application, we find an explicit stratification of the spin moduli space for an odd spin…

Let G be a connected semisimple linear algebraic group over an algebraically closed field k of positive characteristic and let X denote an equivariant embedding of G. We define a distinguished Steinberg fiber N in G, called the zero-fiber,…

The moduli space $\mathcal{A}_g$ of principally polarised abelian varieties of dimension $g$, defined over an algebraically closed field of characteristic $p >0$, is studied through various stratifications. The two most prominent ones are…

We consider the topology for a class of hypersurfaces with highly nonisolated singularites which arise as exceptional orbit varieties of a special class of prehomogeneous vector spaces, which are representations of linear algebraic groups…

Given a family of cyclic covers of $\mathbb{P}^1$ and a prime $p$ of good reduction, by [12] the generic Newton polygon (resp. Ekedahl--Oort type) in the family ($\mu$-ordinary) is known. In this paper, we investigate the existence of…

Suppose that g > 2, that n > 0 and that m > 0. In this paper we show that if E is an irreducible smooth variety which dominates a divisor D in M_{g,n}[m], the moduli space of n-pointed, smooth curves of genus g with a level m structure,…

We study Shimura varieties associated with special orthogonal groups over the field of rational numbers. We prove a version of Morel's formula for the Frobenius--Hecke traces on the intersection cohomology of the Baily--Borel…

In this article we study the Ekedahl-Oort types of $\mathbb{Z}/2\mathbb{Z}$-Galois covers $\pi:Y \to X$ in characteristic two. When the base curve $X$ is ordinary, we show that the Ekedahl-Oort type of $Y$ is completely determined by the…

We consider Shimura varieties associated to a unitary group of signature $(n-1, 1)$. For these varieties, we construct $p$-adic integral models over odd primes $p$ which ramify in the imaginary quadratic field with level subgroup at $p$…

We prove the Hecke orbit conjecture of Chai--Oort for Shimura varieties of Hodge type at odd primes of good reduction. We use a novel result for the local monodromy groups of $F$-isocrystals "coming from geometry", which refines Crew's…

In this paper we classify the topological invariants of the possible branch loci of a smooth double cover $f:X\rightarrow Y$ of a K3 surface $Y$. We describe some geometric properties of $X$ which depend on the properties of the branch…

The main result of this paper is the construction of a new class of weight shifting operators, similar to the theta operators of arXiv:1902.10911, arXiv:1712.06969 and others, which are defined on the lower Ekedahl-Oort strata of the…

In this paper we study the reduction of PEL-Shimura varieties associated to unitary groups of signature (n-1,1) in the inert and unramified case. We describe the Newton polygon and the Ekedahl-Oort stratification. We further study the…

We study closures of conjugacy classes in the symmetric matrices of the orthogonal group and we determine which one are normal varieties. In contrast to the result for the symplectic group where all classes have normal closure, there is…

We relate the Brauer group of a smooth variety over a p-adic field to the geometry of the special fibre of a regular model, using the purity theorem in \'etale cohomology. As an illustration, we describe how the Brauer group of a smooth del…