Logarithmic heat projective operators

Xiaotao Sun

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Logarithmic heat projective operators

Xiaotao Sun

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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 $Θ_{S_0}$. We are interested in the problem: to find suitable degeneration $\Cal M_S$ of moduli spaces and extension $Θ_S$ of theta line bundles such that the direct image of $Θ_S$ 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.

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BibTeX RIS

Xiaotao Sun. 2000-09-21. Logarithmic heat projective operators. https://arxiv.org/abs/math/0009196

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