Related papers: Master Spaces for stable pairs

Moduli spaces of semistable torsion-free sheaves on a K3 surface $X$ are often holomorphic symplectic varieties, deformation equivalent to a Hilbert scheme parametrizing zero-dimensional subschemes of $X$. In fact this should hold whenever…

We study moduli spaces $\mathcal{N}$ of rank 2 stable reflexive sheaves on $\mathbb{P}^3$. Fixing Chern classes $c_1$, $c_2$, and summing over $c_3$, we consider the generating function $\mathsf{Z}^{\mathrm{refl}}(q)$ of Euler…

Projective duality identifies the moduli spaces $\mathbf{B}_n$ and $\mathbf{X}(3,n)$ parametrizing linearly general configurations of $n$ points in $\mathbb{P}^2$ and $n$ lines in the dual $\mathbb{P}^2$, respectively. The space…

The theory of moduli of morphisms on P^n generalizes the study of rational maps on P^1. This paper proves three results about the space of morphisms on P^n of degree d > 1, and its quotient by the conjugation action of PGL(n+1). First, we…

We apply virtual localization to the problem of finding blowup formulae for virtual sheaf-theoretic invariants on a smooth projective surface. This leads to a general procedure that can be used to express virtual enumerative invariants on…

In recent papers math.DG/0701278 and arXiv:0705.0060, we gave explicit description of some new Moishezon twistor spaces. In this paper, developing the method in the papers much further, we explicitly give projective models of a number of…

We analyze the relationship between two compactifications of the moduli space of maps from curves to a Grassmannian: the Kontsevich moduli space of stable maps and the Marian--Oprea--Pandharipande moduli space of stable quotients. We…

We give a complete classification of equivariant vector bundles of rank two over smooth complete toric surfaces and construct moduli spaces of such bundles. This note is a direct continuation of an earlier note where we developed a general…

We use Donaldson invariants of regular surfaces with p_g >0 to make quantitative statements about modulispaces of stable rank 2 sheaves. We give two examples: a quantitative existence theorem for stable bundles, and a computation of the…

This informal note provides some elementary examples to motivate the local structural results of [1] on the moduli space of genus one stable maps to projective space. The hope is that these examples will be helpful for graduate students to…

The Gieseker-Uhlenbeck morphism maps the Gieseker moduli space of stable rank-2 sheaves on a smooth projective surface to the Uhlenbeck compactification, and is a generalization of the Hilbert-Chow morphism for Hilbert schemes of points.…

We classify (semi)stable sheaves on a rational curve with one node. The results are based on the classification of indecomposable torsion-free sheaves due to Drozd and Greuel "Tame and wild projective curves and classification of vector…

Motivated by applications to duality theorems for $p$-adic pro-\'etale cohomology of rigid analytic spaces, we study the category of Topological Vector Spaces in the setting of condensed mathematics. We prove that it contains, as full…

We give classifications of linear orbits of pairs of square matrices with non-vanishing discriminant polynomials over a field in terms of certain coherent sheaves with additional data on closed subschemes of the projective line. Our results…

We give a purely algebraic construction of the continuous closure of any finitely generated torsion free module; a concept first studied by H.~Brenner and M.~Hochster. The construction implies that, at least in characteristic 0, taking…

This paper is devoted to the study of some coherent sheaves on non reduced curves that can be locally embedded in smooth surfaces. If Y is such a curve then there is a filtration by subschemes C_i such that C_1 is the reduced curve…

There is a canonical identification, due to the author, of a convex real projective structure on an orientable surface of genus g and a pair consisting of a conformal structure together with a holomorphic cubic differential on the surface.…

Given a vector bundle $F$ on a variety $X$ and $W\subset H^0(F)$ such that the evaluation map $W\otimes \mathcal{O}_X\to F$ is surjective, its kernel $S_{F,W}$ is called generalized syzygy bundle. Under mild assumptions, we construct a…

We construct the derived scheme of stable sheaves on a smooth projective variety via derived moduli of finite graded modules over a graded ring. We do this by dividing the derived scheme of actions of Ciocan-Fontanine and Kapranov by a…

We develop a theory of \emph{reduced} Gromov-Witten and stable pair invariants of surfaces and their canonical bundles. We show that classical Severi degrees are special cases of these invariants. This proves a special case of the MNOP…