Related papers: Stability of Tails and 4-Canonical Models

We construct moduli spaces of linear self-maps of projective space with marked points, up to projective equivalence. That is, we let the special linear group act simultaneously by conjugation on projective linear maps and diagonally on…

We establish GIT semistability of the 2nd Hilbert point of every Gieseker-Petri general canonical curve by a simple geometric argument. As a consequence, we obtain an upper bound on slopes of general families of Gorenstein curves. We also…

In this paper, we study the birational geometry of the Hilbert scheme of n points on P^2. We discuss the stable base locus decomposition of the effective cone and the corresponding birational models. We give modular interpretations to the…

We apply Bridgeland stability conditions machinery to describe the geometry of some classical moduli spaces associated with canonical genus four curves in $\mathbb{P}^3$ via an effective control over its wall-crossing. These moduli spaces…

We consider the action of a semisimple subgroup $\hat G$ of a semisimple complex group $G$ on the flag variety $X=G/B$, and the linearizations of this action by line bundles $\mathcal L$ on $X$. The main result is an explicit description of…

We construct the Mumford-Knudsen space of n pointed stable rational curves by a sequence of explicit blow-ups from the GIT quotient (P^1)^n//SL(2) with respect to the symmetric linearization O(1,...,1). The intermediate blown-up spaces turn…

We study the GIT quotient of the symplectic grassmannian parametrizing lagrangian subspaces of \bigwedge^3{\mathbb C}^6 by the natural action of SL_6, call it M. This is a compactification of the moduli space of smooth double EPW-sextics.…

We study double-sided actions of $(\mathbb{C}^*)^2$ on $SL(3,\mathbb{C})/U$ and the associated quotients, where $U$ is a maximal unipotent subgroup of $SL(3,\mathbb{C})$. The main results of this paper are a sufficient condition for the…

We compute the class of the locus in M_g of curves having a pencil with two unspecified triple ramification points. This is the first example of a geometric divisor on M_g which is not the pull-back of a divisor on the moduli space of…

We prove by Hilbert-Mumford criterion that a slope stable polarized weighted pointed nodal curve is Chow asymptotic stable. This generalizes the result of Caporaso on stability of polarized nodal curves, and of Hasset on weighted pointed…

Let $X\subset \mathbb P^n$ be a degree $d$ hypersurface. We prove that $X$ is GIT stable if the minimal exponent $\widetilde \alpha(X)>\frac{n+1}{d}$ and GIT semistable if $\widetilde \alpha(X)=\frac{n+1}{d}$, resolving a question of Laza.…

This paper is the first in a series of four papers aiming to describe the (almost integral) Chow ring of $\bar{\mathcal{M}}_3$, the moduli stack of stable curves of genus $3$. In this paper, we introduce the moduli stack…

We study the GIT compactification $\mathbb{P}(\mathrm{Sym}^3\mathbb{C}^7)//\mathrm{SL}(7)$ of the moduli space of cubic fivefolds $X\subset\mathbb{P}^6$ and give an explicit description of its strictly semistable boundary. We construct…

A moduli space of stable quotients of the rank n trivial sheaf on stable curves is introduced. Over nonsingular curves, the moduli space is Grothendieck's Quot scheme. Over nodal curves, a relative construction is made to keep the torsion…

We perform a variation of geometric invariant theory stability analysis for 2nd Hilbert points of bi-log-canonically embedded pointed curves of genus two. As a result, we give a GIT construction of the last three non-trivial log canonical…

As a continuation of the work of Freiermuth and Trautmann, we study the geometry of the moduli space of stable sheaves on $\mathbb{P}^3$ with Hilbert polynomial $4m+1$. The moduli space has three irreducible components whose generic…

We consider a notion of stability for sheaves, which we call multi-Gieseker stability that depends on several ample polarisations $L_1, \dots, L_N$ and on an additional parameter $\sigma \in \mathbb{Q}_{\geq 0}^N\setminus\{0\}$. The set of…

In this paper, we consider the GIT quotients of Schubert varieties for the action of a maximal torus. We describe the minuscule Schubert varieties for which the semistable locus is contained in the smooth locus. As a consequence, we study…

We study the moduli space of stable sheaves of Euler characteristic 1 supported on curves of arithmetic genus 3 contained in a smooth quadric surface. We show that this moduli space is rational. We compute its Betti numbers by studying the…

S. Kondo has constructed a ball quotient compactification for the moduli space of non-hyperelliptic genus four curves. In this paper, we show that this space essentially coincides with a GIT quotient of the Chow variety of canonically…