Counting h0(D) on primary Burniat surfaces

초록

We study the cohomology of divisors on a Burniat surface X with K2X = 6. We provide an algorithm for computing the cohomology groups of arbitrary divisors on X. As an application, we prove that there are no Ulrich line bundles (with respect to an arbitrary polarization), and that there exists an Ulrich vector bundle of rank 2 with respect to 3KX. The existence of Ulrich vector bundle of rank 2 was previously established by Casnati, but our construction yields one that cannot be obtained by his method. (c) 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

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