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slope of a coherent sheaf

Contents

Context

Topos Theory

topos theory

Background

Toposes

Internal Logic

Topos morphisms

Extra stuff, structure, properties

Cohomology and homotopy

In higher category theory

Theorems

Homological algebra

homological algebra

(also nonabelian homological algebra)

Introduction

Context

Basic definitions

Stable homotopy theory notions

Constructions

Lemmas

diagram chasing

Homology theories

Theorems

Contents

Definition

A rational number associated with a coherent sheaf EE over a curve: the degree divided by the rank:

μ(E)deg(E)rank(E). \mu(E) \;\coloneqq\; \frac{deg(E)}{rank(E)} \,.

For vector bundles: “normalized Chern character” (Shatz 77)

e.g. (Huybrechts-Lehn 96, def. 1.2.11)

This is what enters the condition on stable coherent sheaves.

References

Last revised on October 3, 2018 at 10:49:12. See the history of this page for a list of all contributions to it.