Yonghwa Cho, Cohomology of Divisors on Burniat Surfaces

A (primary) Burniat surface is a complex surface of general type that can be obtained as a bidouble cover of del Pezzo surface with K² = 6. The Picard group is an abelian group of rank 4 with torsion part isomorphic to (Z/2)⁶. Alexeev studied the divisors on Burniat surfaces, and observed that the irreducible components of ramification divisors span the semigroup of effective divisors. Based on Alexeev’s result, I will describe the method for computing cohomology of arbitrary divisors on Burniat surfaces. If time permits, (non-)existence question about Ulrich bundles will be discussed as an application.