Logarithmic heat projective operators

2000/09/21 by Xiaotao Sun, Sun, Xiaotao
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Algebraic Geometry (math.AG) #Algebraic and Geometric Analysis #FOS: Mathematics #Matrix Theory and Algorithms #math.AG

paper · pdf · doi:10.48550/arxiv.math/0009196

26 pages, amstex

arxiv created 2000/09/21 · openalex publication_date 2000/09/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f:\Cal C→ S be a flat family of curves over a smooth curve S such that f is smooth over S₀=S\ssm\s₀\ and f^-1(s₀)=\Cal C₀ is irreducible with one node. We have an associated family \Cal M_S0→ S₀ of moduli spaces of semistable vector bundles and the relative theta line bundle Θ_S0. 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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