Counting $h^0(D)$ on primary Burniat surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914407780450304 |
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| author | Cho, Yonghwa |
| author_facet | Cho, Yonghwa |
| contents | We study the cohomology of divisors on a Burniat surface $X$ with $K_X^2=6$. 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 $3K_X$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18240 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Counting $h^0(D)$ on primary Burniat surfaces Cho, Yonghwa Algebraic Geometry We study the cohomology of divisors on a Burniat surface $X$ with $K_X^2=6$. 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 $3K_X$. 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. |
| title | Counting $h^0(D)$ on primary Burniat surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2512.18240 |