Hostname: page-component-5b777bbd6c-2c8nx Total loading time: 0 Render date: 2025-06-22T08:01:25.872Z Has data issue: true hasContentIssue false
  • English
  • Français

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

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

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
Get access Rights & Permissions [Opens in a new window]

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
Check for updates
Copyright
© (2021) The Authors. The publishing rights in this article are licenced to Foundation Nagoya Mathematical Journal under an exclusive license

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

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