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June 2017 A Remark on the Deformation Equivalence Classes of Hopf Surfaces
Shota MURAKAMI
Tokyo J. Math. 40(1): 237-245 (June 2017). DOI: 10.3836/tjm/1502179225

Abstract

Let $S$ be a compact complex surface. With the exception of some complex surfaces, it is known that there are only finitely many deformation types of complex surfaces with the same homotopy type as $S$. Let $\mathcal{H}(S)$ be the set of deformation equivalence classes of complex surfaces homotopy equivalent to $S$. We evaluate $\# \mathcal{H}(S)$ when $S$ is a Hopf surface. As a corollary, we construct a sequence of Hopf surfaces $(S_n)$ such that although $\# \mathcal{H}(S_n)$ is finite for all $n$, the sequence $(\# \mathcal{H}(S_n))$ is unbounded.

Citation

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Shota MURAKAMI. "A Remark on the Deformation Equivalence Classes of Hopf Surfaces." Tokyo J. Math. 40 (1) 237 - 245, June 2017. https://doi.org/10.3836/tjm/1502179225

Information

Published: June 2017
First available in Project Euclid: 8 August 2017

zbMATH: 1376.32022
MathSciNet: MR3689988
Digital Object Identifier: 10.3836/tjm/1502179225

Subjects:
Primary: 32J15
Secondary: 14J25

Rights: Copyright © 2017 Publication Committee for the Tokyo Journal of Mathematics

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Vol.40 • No. 1 • June 2017
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