Mathematical Society of Japan Memoirs

Chapter 1. Stable sheaves

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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

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

First available in Project Euclid: 1 July 2016

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Copyright © 2016, The Mathematical Society of Japan


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.

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