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CONICS IN SEXTIC $K3$-SURFACES IN $\mathbb {P}^4$

Part of: Curves Surfaces and higher-dimensional varieties Projective and enumerative geometry

Published online by Cambridge University Press:  29 November 2021

ALEX DEGTYAREV Open the ORCID record for ALEX DEGTYAREV [Opens in a new window]
ALEX DEGTYAREV*
Affiliation:
Department of Mathematics Bilkent University06800Ankara, Turkeydegt@fen.bilkent.edu.tr
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Abstract

We prove that the maximal number of conics in a smooth sextic $K3$ -surface $X\subset \mathbb {P}^4$ is 285, whereas the maximal number of real conics in a real sextic is 261. In both extremal configurations, all conics are irreducible.

MSC classification

Primary: 14J28: $K3$ surfaces and Enriques surfaces
Secondary: 14H50: Plane and space curves 14N20: Configurations and arrangements of linear subspaces 14N25: Varieties of low degree
Type
Article
Information
Nagoya Mathematical Journal , Volume 246 , June 2022 , pp. 273 - 304
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Copyright
© (2021) The Authors. The publishing rights in this article are licenced to Foundation Nagoya Mathematical Journal under an exclusive license

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Footnotes

The author was partially supported by the TÜBİTAK grant 118F413.

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