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LOGARITHMIC HEAT PROJECTIVE OPERATORS

Authors :
Xiaotao Sun
Source :
Communications in Algebra. 33:425-454
Publication Year :
2005
Publisher :
Informa UK Limited, 2005.

Abstract

Let $f:\Cal C\to S$ be a flat family of curves over a smooth curve $S$ such that $f$ is smooth over $S_0=S\ssm\{s_0\}$ and $f^{-1}(s_0)=\Cal C_0$ is irreducible with one node. We have an associated family $\Cal M_{S_0}\to S_0$ of moduli spaces of semistable vector bundles and the relative theta line bundle $\Theta_{S_0}$. We are interested in the problem: to find suitable degeneration $\Cal M_S$ of moduli spaces and extension $\Theta_S$ of theta line bundles such that the direct image of $\Theta_S$ is a vector bundle on $S$ with a logarithmic projective connection. In this paper, we figured out the conditions of existence of the connection and solved the problem for rank one.<br />Comment: 26 pages, amstex

Details

ISSN :
15324125 and 00927872
Volume :
33
Database :
OpenAIRE
Journal :
Communications in Algebra
Accession number :
edsair.doi.dedup.....6e920ac3c89b83d5e05802edfa100159
Full Text :
https://doi.org/10.1081/agb-200047410