Related papers: The Locus of Plane Quartics with A Hyperflex

We show that the moduli space M of marked cubic surfaces is biholomorphic to the quotient by a discrete group generated by complex reflections of the complex four-ball minus the reflection hyperplanes of the group. Thus M carries a complex…

Consider the 1-dimensional Hurwitz space parameterizing covers of P^1 branched at four points. We study its intersection with divisor classes on the moduli space of curves. As an application, we calculate the slope of the Teichmuller curve…

The flex divisor of a primitively polarized K3 surface $(X,L)$ of degree $L^2=2d$ is, generically, the locus of all points $x\in X$ for which there exists a pencil $V\subset |L|$ whose base locus is $\{x\}$. We show that the flex divisor…

Let O be a maximal order in a totally indefinite quaternion algebra over a totally real number field. In this note we study the locus Q_O of quaternionic multiplication by O in the moduli space A_g of principally polarized abelian varieties…

It is known that the moduli space of plane quartic curves is birational to an arithmetic quotient of a 6-dimensional complex ball. In this paper, we shall show that there exists a 15-dimensional space of meromorphic automorphic forms on the…

We construct an infinite number of Shimura curves contained in the locus of hyperelliptic Jacobians of genus 3. In the opposite direction, we show that in genus 3 the only possible non-complete (in the moduli space of abelian threefolds)…

We study the Hausdorff distance between a set and its convex hull. Let $X$ be a Banach space, define the CHD-module of space $X$ as the supremum of this distance for all subset of the unit ball in $X$. In the case of finite dimensional…

In Cogdell et al., \it LMS Lecture Notes Series \bf 459, \rm 393--427 (2020), \rm the authors proved an analogue of Kronecker's limit formula associated to any divisor $\mathcal D$ which is smooth in codimension one on any smooth K\"ahler…

Given a smooth plane curve $\overline{C}$ of genus $g\geq 3$ over an algebraically closed field $\overline{k}$, a field $L\subseteq\overline{k}$ is said to be a \emph{plane model-field of definition for $\overline{C}$} if $L$ is a field of…

We construct a moduli space of stable maps with fields associated to a triple $(X,E,s)$ of a projective variety (or a DM stack with projective moduli space) a vector bundle and a section. We show the class coincides up to a sign with the…

We study the moduli space of discrete, faithful, type-preserving representations of the modular group $\mathbf{PSL}(2,\mathbb{Z})$ into $\mathbf{PU}(3,1)$. The entire moduli space $\mathcal{M}$ is a union of…

We study genus $g$ coverings of full moduli dimension of degree $d=[\frac {g+3} 2]$. There is a homomorphism between the corresponding Hurwitz space $\H$ of such covers to the moduli space $\M_g$ of genus $g$ curves. In the case $g=3$,…

We decompose each moduli space of semistable sheaves on the complex projective plane with support of dimension one and degree four into locally closed subvarieties, each subvariety being the good or geometric quotient of a set of morphisms…

We investigate two families of divisors which we expect to play a distinguished role in the global geometry of Hurwitz space. In particular, we show that they are extremal and rigid in the small degree regime $d \leq 5$. We further show…

We consider a moduli space of lattice polarized K3 surfaces with the additional information of a frame of the trascendental cohomology with respect to the lattice polarization. This moduli space is proved to be quasi-affine, and the…

This paper explores the cohomological consequences of the existence of moduli spaces for flat bundles with bounded rank and irregularity at infinity and gives unconditional proofs. Namely, we prove the existence of a universal bound for the…

We study the Kuznetsov component of cubic fivefolds via their quadric fibration model, and construct a family of Serre-invariant Bridgeland stability conditions on it. For every primitive numerical class, we prove that the associated…

This paper extends joint work with R. Friedman to show that the closure of the locus of intermediate Jacobians of smooth cubic threefolds, in the moduli space of principally polarized abelian varieties (ppav's) of dimension five, is an…

We study some particular loci inside the moduli space $\mathcal{M}_g$, namely the bielliptic locus (i.e. the locus of curves admitting a $2:1$ cover over an elliptic curve $E$) and the bihyperelliptic locus (i.e. the locus of curves…

We describe the final log canonical model of the moduli space of stable curves of genus four. We prove that the rational map from $\bar{M}_4$ to this model contracts the Petri and the boundary divisors and flips the hyperelliptic locus. As…