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arXiv · 2001.07952

Brill-Noether general K3 surfaces with the maximal number of elliptic pencils of minimal degree

Michael Hoff·Andreas Leopold Knutsen
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Abstract

We explicitly construct Brill--Noether general $K3$ surfaces of genus $4,6$ and $8$ having the maximal number of elliptic pencils of degrees $3, 4$ and $5$, respectively, and study their moduli spaces and moduli maps to the moduli space of curves. As an application we prove the existence of Brill--Noether general $K3$ surfaces of genus $4$ and $6$ without stable Lazarsfeld--Mukai bundles of minimal $c_2$.

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Michael Hoff, Andreas Leopold Knutsen. 2020-01-22. Brill-Noether general K3 surfaces with the maximal number of elliptic pencils of minimal degree. https://arxiv.org/abs/2001.07952

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