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On the moduli of stable sheaves on a reducible projective scheme and examples on a reducible quadric surface. (English) Zbl 1056.14014
Summary: We study the moduli space of stable sheaves on a reducible projective scheme by use of a suitable stratification of the moduli space. Each stratum is the moduli space of “triples”, which is the main object investigated in this paper. As an application, we can see that the relative moduli space of rank two stable sheaves on quadric surfaces gives a nontrivial example of the relative moduli space which is not flat over the base space.

MSC:
14D20 Algebraic moduli problems, moduli of vector bundles
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
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