Mathematical Society of Japan Memoirs

Chapter 1. Stable sheaves

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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

Chapter information

Source
Masaki Maruyama,Moduli spaces of stable sheaves on schemes (Tokyo: The Mathematical Society of Japan, 2016), 1-23

Dates
First available in Project Euclid: 1 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.msjm/1467400248

Digital Object Identifier
doi:10.2969/msjmemoirs/03301C010

Rights
Copyright © 2016, The Mathematical Society of Japan

Citation

Maruyama, Masaki. Chapter 1. Stable sheaves. Moduli spaces of stable sheaves on schemes, 1--23, The Mathematical Society of Japan, Tokyo, Japan, 2016. doi:10.2969/msjmemoirs/03301C010. https://projecteuclid.org/euclid.msjm/1467400248


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