Tokyo Journal of Mathematics

A Remark on the Deformation Equivalence Classes of Hopf Surfaces


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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.

Article information

Tokyo J. Math., Volume 40, Number 1 (2017), 237-245.

First available in Project Euclid: 8 August 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32J15: Compact surfaces
Secondary: 14J25: Special surfaces {For Hilbert modular surfaces, see 14G35}


MURAKAMI, Shota. A Remark on the Deformation Equivalence Classes of Hopf Surfaces. Tokyo J. Math. 40 (2017), no. 1, 237--245. doi:10.3836/tjm/1502179225.

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