Related papers: The non-existence of stable Schottky forms

We prove that the moduli stack of stable curves of genus g with n marked points is rigid, i.e., has no infinitesimal deformations. This confirms the first case of a principle proposed by Kapranov. It can also be viewed as a version of…

In this paper, we prove that the moduli space $\overline{M}_{X}(\nu)$ of $H$-Gieseker semistable sheaves on a smooth cubic threefold $X$ with Chern character $\nu=(4,-H,-\frac{5}{6}H^{2},\frac{1}{6}H^{3})$ is non-empty, smooth and…

Considering the so-called Simpson system on smooth projective varieties, defined over an algebraically closed field of characteristic 0, whose canonical bundle is ample, I give another proof the stability of this Higgs bundle, from which…

This work seeks to advance the understanding of the smooth structure of the moduli space of self-dual contact instantons (SDCI) on Sasakian 7-manifolds M. A neighborhood of a smooth point of M is locally modeled on the first cohomological…

We prove a localization formula for the moduli space of stable relative maps. As an application, we prove that all codimension i tautological classes on the moduli space of stable pointed curves vanish away from strata corresponding to…

We study open orbits of symmetric subgroups of a simple connected Lie group G on a causal flag manifold. First we show that a flag manifold M of G carries an invariant causal structure if and only if G is hermitian of tube type and M is the…

Perfect quadratic forms give a toroidal compactification of the moduli space of principally polarized abelian g-folds that is Q-factorial and whose ample classes are characterized, over any base. In characteristic zero it has canonical…

We introduce the moduli space of quasi-parabolic $SL(2,\mathbb{C})$-Higgs bundles over a compact Riemann surface $\Sigma$ and consider a natural involution, studying its fixed point locus when $\Sigma$ is $\mathbb{C} \mathbb{P}^1$ and…

We prove that the cohomology of the moduli space of morphisms of a fixed finite degree from a smooth projective curve $C$ of genus $g$ to a complete simplicial toric variety $\mathbb{P}(\Sigma)$, denoted by the rational polyhedral fan…

Consider a compact manifold $N$ (with or without boundary) of dimension $n$. Positive $m$-intermediate curvature interpolates between positive Ricci curvature ($m = 1$) and positive scalar curvature ($m = n-1$), and it is obstructed on…

We relate the theory of moduli spaces $\overline{\mathcal{M}}_{0,\mathcal{A}}$ of stable weighted curves of genus $0$ to the equivariant topology of complex Grassmann manifolds $G_{n,2}$, with the canonical action of the compact torus…

There are $75$ moduli spaces $F_S$ of K3 surfaces with a nonsymplectic involution. We give detailed descriptions of Kulikov models for one-parameter degenerations in $F_S$. In the $50$ cases where the fixed locus of the involution has a…

Let $X$ be a compact connected Riemann surface of genus $g$, with $g\, \geq\,2$, and let $\xi$ be a holomorphic line bundle on $X$ with $\xi^{\otimes 2}\,=\, {\mathcal O}_X$. Fix a theta characteristic $\mathbb L$ on $X$. Let ${\mathcal…

It is known that every nonorientable surface $\Sigma$ has an orientable double cover $\tilde{\Sigma}$. The covering map induces an involution on the moduli space $\tilde{\M}$ of gauge equivalence classes of flat $G$-connections on…

We construct a canonical compactification $SQ^{toric}_{g,K}$ of the moduli of abelian varieties over $Z[\zeta_N, 1/N]$ where $\zeta_N$ is a primitive $N$-th root of unity. This is very similar to, but slightly diferent from the…

The cherry on top of this stacky paper is the following: for any g>1 we give a finite group G such that the moduli space of connected admissible G-covers of genus g is a smooth, fine moduli space, which is a Galois cover of the moduli space…

In this paper we introduce a new invariant for the action of a finite group $G$ on a compact complex curve of genus $g$. With the aid of this invariant we achieve the classification of the components of the moduli space of curves with an…

For a smooth projective curve $X$ over $\mathbb C_p$ and any reductive group $G$, we show that the moduli stack of $G$-Higgs bundles on $X$ is a twist of the moduli stack of v-topological $G$-bundles on $X_v$ in a canonical way. We explain…

We consider Kobayashi geodesics in the moduli space of abelian varieties A_g that is, algebraic curves that are totally geodesic submanifolds for the Kobayashi metric. We show that Kobayashi geodesics can be characterized as those curves…

In this paper, we investigate the construction of two moduli stacks of Kummer varieties. The first one is the stack $\mathcal K^{\text{abs}}_g$ of abstract Kummer varieties and the second one is the stack $\mathcal K^{\text{em}}_g$ of…