## Advanced Studies in Pure Mathematics

### Divisors on Burniat surfaces

Valery Alexeev

#### Abstract

In this short note, we extend the results of [Alexeev-Orlov, 2012] about Picard groups of Burniat surfaces with $K^2=6$ to the cases of $2\le K^2\le 5$. We also compute the semigroup of effective divisors on Burniat surfaces with $K^2=6$. Finally, we construct an exceptional collection on a nonnormal semistable degeneration of a 1-parameter family of Burniat surfaces with $K^2=6$.

#### Article information

Dates
Revised: 23 February 2014
First available in Project Euclid: 4 October 2018

https://projecteuclid.org/ euclid.aspm/1538622433

Digital Object Identifier
doi:10.2969/aspm/06910287

Mathematical Reviews number (MathSciNet)
MR3586510

Zentralblatt MATH identifier
1369.14050

#### Citation

Alexeev, Valery. Divisors on Burniat surfaces. Development of Moduli Theory — Kyoto 2013, 287--302, Mathematical Society of Japan, Tokyo, Japan, 2016. doi:10.2969/aspm/06910287. https://projecteuclid.org/euclid.aspm/1538622433