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January, 2013 Remarks on surfaces with $c_1^2 =2\chi -1$ having non-trivial 2-torsion
Masaaki MURAKAMI
J. Math. Soc. Japan 65(1): 51-95 (January, 2013). DOI: 10.2969/jmsj/06510051

Abstract

We shall show that any complex minimal surface of general type with $c_1^2 = 2\chi -1$ having non-trivial 2-torsion divisors, where $c_1^2$ and $\chi$ are the first Chern number of a surface and the Euler characteristic of the structure sheaf respectively, has the Euler characteristic $\chi$ not exceeding 4. Moreover, we shall give a complete description for the surfaces of the case $\chi =4$, and prove that the coarse moduli space for surfaces of this case is a unirational variety of dimension 29. Using the description, we shall also prove that our surfaces of the case $\chi = 4$ have non-birational bicanonical maps and no pencil of curves of genus 2, hence being of so called non-standard case for the non-birationality of the bicanonical maps.

Citation

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Masaaki MURAKAMI. "Remarks on surfaces with $c_1^2 =2\chi -1$ having non-trivial 2-torsion." J. Math. Soc. Japan 65 (1) 51 - 95, January, 2013. https://doi.org/10.2969/jmsj/06510051

Information

Published: January, 2013
First available in Project Euclid: 24 January 2013

zbMATH: 1268.14041
MathSciNet: MR3034399
Digital Object Identifier: 10.2969/jmsj/06510051

Subjects:
Primary: 14J29
Secondary: 13J10 , 32G05

Keywords: moduli space , surfaces of general type , torsion group

Rights: Copyright © 2013 Mathematical Society of Japan

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Vol.65 • No. 1 • January, 2013
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