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Divisors on Burniat surfaces. (English) Zbl 1369.14050
Fujino, Osamu (ed.) et al., Development of moduli theory – Kyoto 2013. Proceedings of the 6th Mathematical Society of Japan-Seasonal Institute, MSJ-SI, Kyoto, Japan, June 11–21, 2013. Tokyo: Mathematical Society of Japan (MSJ) (ISBN 978-4-86497-032-7/hbk). Advanced Studies in Pure Mathematics 69, 287-302 (2016).
Summary: In this short note, we extend the results by the author and D. Orlov [Math. Ann. 357, No. 2, 743–759 (2013; Zbl 1282.14030)] about Picard groups of Burniat surfaces with $$K^2=6$$ to the cases of $$2\leq K^2\leq 5$$. 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 one-parameter family of Burniat surfaces with $$K^2=6$$.
For the entire collection see [Zbl 1353.14002].

##### MSC:
 14J29 Surfaces of general type 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010) 14J10 Families, moduli, classification: algebraic theory 18E30 Derived categories, triangulated categories (MSC2010)
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