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September 2009 A note on Todorov surfaces
Carlos Rito
Osaka J. Math. 46(3): 685-693 (September 2009).


Let $S$ be a Todorov surface, i.e., a minimal smooth surface of general type with $q=0$ and $p_{g}=1$ having an involution $i$ such that $S/i$ is birational to a $K3$ surface and such that the bicanonical map of $S$ is composed with $i$. The main result of this paper is that, if $P$ is the minimal smooth model of $S/i$, then $P$ is the minimal desingularization of a double cover of $\mathbb{P}^{2}$ ramified over two cubics. Furthermore it is also shown that, given a Todorov surface $S$, it is possible to construct Todorov surfaces $S_{j}$ with $K^{2}=1,\ldots,K_{S}^{2}-1$ and such that $P$ is also the smooth minimal model of $S_{j}/i_{j}$, where $i_{j}$ is the involution of $S_{j}$. Some examples are also given, namely an example different from the examples presented by Todorov in [9].


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Carlos Rito. "A note on Todorov surfaces." Osaka J. Math. 46 (3) 685 - 693, September 2009.


Published: September 2009
First available in Project Euclid: 26 October 2009

zbMATH: 1204.14018
MathSciNet: MR2583324

Primary: 14J28 , 14J29

Rights: Copyright © 2009 Osaka University and Osaka City University, Departments of Mathematics


Vol.46 • No. 3 • September 2009
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