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Classification of subpencils for hyperplane sections on certain K3 surfaces

Part of: Cycles and subschemes Families, fibrations

Published online by Cambridge University Press:  23 October 2023

Tomokuni Takahashi
Tomokuni Takahashi*
Affiliation:
Section of Liberal Arts and Sciences, National Institute of Technology, Ichinoseki College, Ichinoseki, Iwate, Japan (tomokuni@ichinoseki.ac.jp)
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Abstract

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.

Keywords

hyperplane sectionsnonhyperelliptic curvespencilsHorikawa index

MSC classification

Primary: 14C20: Divisors, linear systems, invertible sheaves
Secondary: 14D06: Fibrations, degenerations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 66 , Issue 4 , November 2023 , pp. 1022 - 1043
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

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