Tokyo Journal of Mathematics

Deformations of a Holomorphic Map and Its Degeneracy Locus

Madoka EBIHARA

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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.

Article information

Source
Tokyo J. Math., Volume 35, Number 2 (2012), 253-277.

Dates
First available in Project Euclid: 23 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1358951317

Digital Object Identifier
doi:10.3836/tjm/1358951317

Mathematical Reviews number (MathSciNet)
MR3058705

Zentralblatt MATH identifier
1274.14007

Subjects
Primary: 14D15: Formal methods; deformations [See also 13D10, 14B07, 32Gxx]

Citation

EBIHARA, Madoka. Deformations of a Holomorphic Map and Its Degeneracy Locus. Tokyo J. Math. 35 (2012), no. 2, 253--277. doi:10.3836/tjm/1358951317. https://projecteuclid.org/euclid.tjm/1358951317


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References

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