## Journal of the Mathematical Society of Japan

### Remarks on surfaces with $c_1^2 =2\chi -1$ having non-trivial 2-torsion

Masaaki MURAKAMI

#### 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.

#### Article information

Source
J. Math. Soc. Japan, Volume 65, Number 1 (2013), 51-95.

Dates
First available in Project Euclid: 24 January 2013

https://projecteuclid.org/euclid.jmsj/1359036449

Digital Object Identifier
doi:10.2969/jmsj/06510051

Mathematical Reviews number (MathSciNet)
MR3034399

Zentralblatt MATH identifier
1268.14041

#### Citation

MURAKAMI, Masaaki. Remarks on surfaces with $c_1^2 =2\chi -1$ having non-trivial 2-torsion. J. Math. Soc. Japan 65 (2013), no. 1, 51--95. doi:10.2969/jmsj/06510051. https://projecteuclid.org/euclid.jmsj/1359036449

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