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A note on the universal family of moduli of stable sheaves. (English) Zbl 0887.14015
In this note, the author considers necessary conditions for the existence of universal families on moduli spaces of stable sheaves of rank 2 on surfaces. On curves, the problem of the existence of universal families on moduli spaces of stable sheaves was completely solved by Ramanan, and Drezet and Narasimhan. The problem has been then solved on the projective plane, in rank 2, by Le Potier. On rational surfaces and surfaces with $$p_g=0$$, in any rank, the problem has been considered by Drezet. By using Li’s results on Betti numbers of moduli spaces, the author treats the case of $$p_g>0$$.
Reviewer: K.Yoshioka (Kobe)

##### MSC:
 14J10 Families, moduli, classification: algebraic theory 14D20 Algebraic moduli problems, moduli of vector bundles 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010) 14D22 Fine and coarse moduli spaces 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
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