Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Semistability conditions defined by ample classes

Damien Mégy, Mihai Pavel, Matei Toma

Abstract

We study a class of semistability conditions defined by a system of ample classes for coherent sheaves over a smooth projective variety. Under some necessary boundedness assumptions, we show the existence of a well-behaved chamber structure for the variation of moduli spaces of sheaves with respect to the change of semistability.

Semistability conditions defined by ample classes

Abstract

We study a class of semistability conditions defined by a system of ample classes for coherent sheaves over a smooth projective variety. Under some necessary boundedness assumptions, we show the existence of a well-behaved chamber structure for the variation of moduli spaces of sheaves with respect to the change of semistability.
Paper Structure (15 sections, 15 theorems, 55 equations)

This paper contains 15 sections, 15 theorems, 55 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Degree functions.
  4. Semistability conditions
  5. Harder-Narasimhan property
  6. A boundedness criterion
  7. The moduli stack of semistable sheaves
  8. Openness of semistability
  9. Universal closedness
  10. Boundedness of semistability
  11. Existence of good moduli spaces of semistable sheaves
  12. Chamber structure
  13. The case of slope-semistability
  14. The case of fixed top degree
  15. The general case

Key Result

Proposition 2.4

Let $\alpha = (\alpha_d,\ldots,\alpha_0)$ be a degree system of ample classes. Then the full subcategory of $\mathop{\mathrm{Coh}}\nolimits(X)$ whose objects are the zero sheaf and all $\alpha$-semistable sheaves of dimension $d$ on $X$ with fixed reduced $\alpha$-Hilbert polynomial $p$ is abelian,

Theorems & Definitions (36)

  • Remark 2.2
  • Definition 2.3
  • Proposition 2.4
  • Example 2.5
  • Example 2.6
  • Remark 2.7
  • Remark 2.8
  • Definition 2.9
  • Proposition 2.10
  • proof
  • ...and 26 more