31 citations · 230 across the 65 of their papers we have counts for
59 papers · 1 filter
Compactifications of the Eisenstein ancestral Deligne-Mostow variety
Klaus Hulek, Shigeyuki Kondo, Yota Maeda
All arithmetic non-compact ball quotients by Deligne-Mostow's unitary monodromy group arise as sub-ball quotients of either of two spaces called ancestral cases, corresponding to G…
The birational geometry of moduli of cubic surfaces and cubic surfaces with a line
Sebastian Casalaina-Martin, Samuel Grushevsky, Klaus Hulek
We determine the cones of effective and nef divisors on the toroidal compactification of the ball quotient model of the moduli space of complex cubic surfaces with a chosen line. F…
Moduli of polarized Enriques surfaces -- computational aspects
Mathieu Dutour Sikirić, Klaus Hulek
Moduli spaces of (polarized) Enriques surfaces can be described as open subsets of modular varieties of orthogonal type. It was shown by Gritsenko and Hulek that there are, up to i…
Revisiting the moduli space of 8 points on
Klaus Hulek, Yota Maeda
The moduli space of points on , a so-called ancestral Deligne-Mostow space, is, by work of Kondō, also a moduli space of K3 surfaces. We prove that the Deligne-Mo…
Non-isomorphic smooth compactifications of the moduli space of cubic surfaces
Sebastian Casalaina-Martin, Samuel Grushevsky, Klaus Hulek +1
The moduli space of complex cubic surfaces has three different, but isomorphic, compact realizations: as a GIT quotient, as a Baily--Borel compactification of a ball quotient, and…
Moduli of elliptic surfaces: monodromy and Shimada root lattice strata
Klaus Hulek, Michael Lönne
In this paper we investigate two stratifications of the moduli space of elliptically fibred K3 surfaces. The first comes from Shimada's classification of connected components of el…
On the GHKS compactification of the moduli space of K3 surfaces of degree two
Klaus Hulek, Christian Lehn, Carsten Liese
We investigate a toroidal compactification of the moduli space of K3 surfaces of degree originating from the program formulated by Gross-Hacking-Keel-Siebert. This construction…
On the cone of effective surfaces on
Samuel Grushevsky, Klaus Hulek
We determine five extremal effective rays of the four-dimensional cone of effective surfaces on the toroidal compactification of the moduli space ${\mathc…
The Mori fan of the Dolgachev-Nikulin-Voisin family in genus
Klaus Hulek, Carsten Liese
In this paper we study the Mori fan of the Dolgachev-Nikulin-Voisin family in degree as well as the associated secondary fan. The main result is an enumeration of all maximal d…
Relative VGIT and an application to degenerations of Hilbert schemes
Lars H. Halle, Klaus Hulek, Ziyu Zhang
We generalize the classical semi-continuity theorem for GIT (semi)stable loci under variations of linearizations to a relative situation of an equivariant projective morphism from…
Cohomology of the moduli space of cubic threefolds and its smooth models
Sebastian Casalaina-Martin, Samuel Grushevsky, Klaus Hulek +1
We compute and compare the (intersection) cohomology of various natural geometric compactifications of the moduli space of cubic threefolds: the GIT compactification and its Kirwan…
The Euler number of hyper-Kähler manifolds of OG10 type
Klaus Hulek, Radu Laza, Giulia Saccà
Using the Laza-Saccà-Voisin construction, we give a simple proof for the fact that the Euler characteristic of a hyper-Kähler manifold of OG10 type is 176,904, a result previously…
The geometry of degenerations of Hilbert schemes of points
Martin G. Gulbrandsen, Lars H. Halle, Klaus Hulek +1
Given a strict simple degeneration the first three authors previously constructed a degeneration of the relative degree Hilbert scheme of $0…
The topology of and its compactifications
Klaus Hulek, Orsola Tommasi
We survey old and new results about the cohomology of the moduli space of principally polarized abelian varieties of genus and its compactifications. The main emphasis li…
On the Picard numbers of abelian varieties
Klaus Hulek, Roberto Laface
We study the possible Picard numbers of abelian varieties of given dimension . If denotes the set of realizable Picard numbers, then is bounded by . We show tha…
Stable Betti numbers of (partial) toroidal compactifications of the moduli space of abelian varieties
Samuel Grushevsky, Klaus Hulek, Orsola Tommasi
We present an algorithm for explicitly computing the number of generators of the stable cohomology algebra of any rationally smooth partial toroidal compactification of ${\mathcal…
A GIT construction of degenerations of Hilbert schemes of points
Martin G. Gulbrandsen, Lars H. Halle, Klaus Hulek
We present a Geometric Invariant Theory (GIT) construction which allows us to construct good projective degenerations of Hilbert schemes of points for simple degenerations. A compa…
The intersection cohomology of the Satake compactification of for
Samuel Grushevsky, Klaus Hulek
We completely determine the intersection cohomology of the Satake compactifications of the moduli space of principally polarized abelian varieties in genera 2,3,4, except for the d…
Complete moduli of cubic threefolds and their intermediate Jacobians
Sebastian Casalaina-Martin, Samuel Grushevsky, Klaus Hulek +1
The intermediate Jacobian map, which associates to a smooth cubic threefold its intermediate Jacobian, does not extend to the GIT compactification of the space of cubic threefolds,…
Moduli of polarized Enriques surfaces
Valery Gritsenko, Klaus Hulek
In this paper we consider moduli spaces of polarized and numerically polarized Enriques surfaces. The moduli spaces of numerically polarized Enriques surfaces can be described as o…
A relative Hilbert-Mumford criterion
Martin G. Gulbrandsen, Lars H. Halle, Klaus Hulek
We generalize the classical Hilbert-Mumford criteria for GIT (semi-)stability in terms of one parameter subgroups of a linearly reductive group G over a field k, to the relative si…
Extending the Prym map to toroidal compactifications of the moduli space of abelian varieties
Sebastian Casalaina-Martin, Samuel Grushevsky, Klaus Hulek +1
The main purpose of this paper is to present a conceptual approach to understanding the extension of the Prym map from the space of admissible double covers of stable curves to dif…
Stable cohomology of the perfect cone toroidal compactification of
Samuel Grushevsky, Klaus Hulek, Orsola Tommasi
We show that the cohomology of the perfect cone (also called first Voronoi) toroidal compactification of the moduli space of complex principally polarized abelian varieties stabili…
Smoothness and singularities of the perfect form and the second Voronoi compactification of
Mathieu Dutour Sikirić, Klaus Hulek, Achill Schürmann
We study the cones in the first Voronoi or perfect cone decomposition of quadratic forms with respect to the question which of these cones are basic or simplicial. As a consequence…