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December 2012 Deformations of a Holomorphic Map and Its Degeneracy Locus
Madoka EBIHARA
Tokyo J. Math. 35(2): 253-277 (December 2012). DOI: 10.3836/tjm/1358951317

Abstract

Let $f: X \to Y$ be a surjective holomorphic map of compact complex manifolds and $\Delta$ the degeneracy locus of $f$. In this paper we shall discuss relationship between infinitesimal deformations of $f$ and the corresponding infinitesimal displacements of $\Delta$ in $Y$. We shall prove that two kinds of Kodaira-Spencer maps are compatible under certain assumptions. As an application of our main theorem, deformations of quadric bundles shall be discussed.

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Madoka EBIHARA. "Deformations of a Holomorphic Map and Its Degeneracy Locus." Tokyo J. Math. 35 (2) 253 - 277, December 2012. https://doi.org/10.3836/tjm/1358951317

Information

Published: December 2012
First available in Project Euclid: 23 January 2013

zbMATH: 1274.14007
MathSciNet: MR3058705
Digital Object Identifier: 10.3836/tjm/1358951317

Subjects:
Primary: 14D15

Rights: Copyright © 2012 Publication Committee for the Tokyo Journal of Mathematics

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Vol.35 • No. 2 • December 2012
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