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horikawa index

Proceedings of the Edinburgh Mathematical Society (1)

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Classification of subpencils for hyperplane sections on certain K3 surfaces
Part of
- Cycles and subschemes
- Families, fibrations
Tomokuni Takahashi
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 66 / Issue 4 / November 2023

Published online by Cambridge University Press:

23 October 2023, pp. 1022-1043
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We classify the subpencils of complete linear systems for the hyperplane sections on K3 surfaces obtained as the complete intersection of a hyperquadric and a hypercubic. The classification is done from three points of view, namely, the type of a general fibre, the base locus and the Horikawa index of the essential member. This classification shows the distinct phenomenons depending on the rank of the hyperquadrics containing the surface.