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arXiv · 2306.11664

Curves on Brill-Noether special K3 surfaces

Richard Haburcak
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Abstract

Mukai showed that projective models of Brill-Noether general polarized K3 surfaces of genus $6-10$ and $12$ are obtained as linear sections of projective homogeneous varieties, and that their hyperplane sections are Brill-Noether general curves. In general, the question, raised by Knutsen, and attributed to Mukai, of whether the Brill-Noether generality of any polarized K3 surface $(S,H)$ is equivalent to the Brill-Noether generality of smooth curves $C$ in the linear system $|H|$, is still open. Using Lazarsfeld-Mukai bundle techniques, we answer this question in the affirmative for polarized K3 surfaces of genus $\leq 19$, which provides a new and unified proof even in the genera where Mukai models exist.

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Richard Haburcak. 2023-06-20. Curves on Brill-Noether special K3 surfaces. https://doi.org/10.1002/mana.202300403

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