Related papers: Ekedahl-Oort strata in the supersingular locus

In this article, we prove that a version of Tate conjectures for certain Deligne-Lusztig varieties implies the Kudla-Rapoport conjecture for unitary Shimura varieties with maximal parahoric level at unramified primes. Furthermore, we prove…

This work deals with the topological classification of singular foliation germs on $(\mathbb C^{2},0)$. Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho-Sad indices and the…

This text presents several aspects of the theory of equisingularity of complex analytic spaces from the standpoint of Whitney conditions. The goal is to describe from the geometrical, topological, and algebraic viewpoints a canonical…

This paper concerns the characteristic-$p$ fibers of $\mathsf{GU}(q-2,2)$ Shimura varieties, which classify abelian varieties with additional structure. These Shimura varieties admit two stratifications of interest: the Ekedahl-Oort…

We introduce Hochschild (co-)homology of morphisms of schemes or analytic spaces and study its fundamental properties. In analogy with the cotangent complex we introduce the so called (derived) Hochschild complex of a morphism; the…

Utilizing previously established results concerning costratification in relative tensor-triangular geometry, we classify the colocalizing subcategories of the singularity category of a locally hypersurface ring and then we generalize this…

We prove the equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic. This verifies a conjecture made by Rapoport and implies that the results of Nie and Zhou-Zhu can be extended to the whole irreducible components of…

The discriminant, $D$, in the base of a miniversal deformation of an irreducible plane curve singularity, is partitioned according to the genus of the (singular) fibre, or, equivalently, by the sum of the delta invariants of the singular…

This paper studies affine Deligne-Lusztig varieties in the affine flag manifold of a split group. Among other things, it proves emptiness for certain of these varieties, relates some of them to those for Levi subgroups, extends previous…

This paper is a sequel to [He7]. There a notion of marking of isolated hypersurface singularities was defined, and a moduli space $M_\mu^{mar}$ for marked singularities in one $\mu$-homotopy class of isolated hypersurface singularities was…

For a compact Hausdorff space $K$, we give descriptions of the dual of $C(K)^\delta$, the Dedekind completion of the Banach lattice $C(K)$ of continuous, real-valued functions on $K$. We characterize those functionals which are…

Let $X \subset\mathbb{P}^r$ be a projective $d$-variety with isolated determinantal singularities and $\omega$ be a $1$-form on $X$ with a finite number of singularities (in the stratified sense). Under some technical conditions on $r$ we…

Let G be a connected reductive algebraic group over an algebraically closed field k. We consider the strata in G defined by Lusztig as fibers of a map given in terms truncated induction of Springer representations. We extend to arbitrary…

All varieties, extremal contractions, singularities are divided on exceptional and non-exceptional ones. Roughly speaking, there are the infinite families of non-exceptional varieties, extremal contractions or singularities and only the…

In his recent investigation of a super Teichm\"uller space, Sachse (2007), based on work of Molotkov (1984), has proposed a theory of Banach supermanifolds using the `functor of points' approach of Bernstein and Schwarz. We prove that the…

We propose two conjectures on a moduli theoretic approach to constructing Lagrangian subvarieties of hyperk\"ahler varieties arising from the Kuznetsov components of cubic fourfolds or Gushel--Mukai fourfolds. Then we verify the conjectures…

We enumerate the ends of each stratum of meromorphic 1-forms on Riemann surfaces with prescribed multiplicities of zeroes and poles. Our proof uses degeneration techniques based on the construction by…

We give a Kodaira-type classification of general singular fibers of a holomorphic Lagrangian fibration in Fujiki's class $\mathcal C$. Our approach is based on the study of the characteristic vector field of the discriminantal hypersurface,…

In this informal expository note, we quickly introduce and survey compactifications of strata of holomorphic 1-forms on Riemann surfaces, i.e. spaces of translation surfaces. In the last decade, several of these have been constructed,…

We study singular hyperkahler quotients of the cotangent bundle of a complex semisimple Lie group as stratified spaces whose strata are hyperkahler. We focus on one particular case where the stratification satisfies the frontier condition…