January, 2024 Obstructions to deforming maps from curves to surfaces
Takeo NISHINOU
Author Affiliations +
J. Math. Soc. Japan 76(1): 51-71 (January, 2024). DOI: 10.2969/jmsj/86878687

Abstract

This paper studies the obstructions to deforming a map from a complex variety to another variety which is an immersion of codimension one. We extend the classical notion of semiregularity of subvarieties to maps between varieties, and prove the unobstructedness of the deformation of such a map, even when the image is non-reduced. As an application, we give a simple but effective criterion for the vanishing of the obstructions to equisingular deformations of nodal curves on surfaces.

Funding Statement

The author is supported by JSPS KAKENHI Grant Number 18K03313.

Citation

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Takeo NISHINOU. "Obstructions to deforming maps from curves to surfaces." J. Math. Soc. Japan 76 (1) 51 - 71, January, 2024. https://doi.org/10.2969/jmsj/86878687

Information

Received: 25 April 2021; Revised: 4 June 2022; Published: January, 2024
First available in Project Euclid: 8 February 2023

Digital Object Identifier: 10.2969/jmsj/86878687

Subjects:
Primary: 32G10
Secondary: 32J15

Keywords: deformation theory , semiregularity

Rights: Copyright ©2024 Mathematical Society of Japan

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Vol.76 • No. 1 • January, 2024
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