Brill–Noether general K3 surfaces with the maximal number of elliptic pencils of minimal degree
Journal article, Peer reviewed
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Original versionGeometriae Dedicata. 2020 10.1007/s10711-020-00565-z
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 c2.