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VOL. 33 | 2016 Chapter 1. Stable sheaves

Abstract

First we shall show that if we collect all the vector bundles on a projective variety and require a weak universal property of a moduli space, then there does not exist the moduli space. This motivates us to introduce the notion of stability and semi-stability. The idea of Harder-Narasimhan filtration plays a crucial role sometimes behind strong results and sometimes very explicitly. Two of basic results on boundedness are proved in the section 3. The formulation of the first is due to L. S. Kleiman [K2] and the second is a theorem of Grothendieck [G]. We shall show a beautiful application of the second result in the proof of the openness of stability

Information

Published: 1 January 2016
First available in Project Euclid: 1 July 2016

Digital Object Identifier: 10.2969/msjmemoirs/03301C010

Rights: Copyright © 2016, The Mathematical Society of Japan

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