Smooth rational curves on Enriques surfaces
type: Item
instance of: scholarly article
title: Smooth rational curves on Enriques surfaces
zbMATH Open document ID: 0545.14024
DOI: 10.1007/BF01455565
author: François R. Cossec
author: Igor V. Dolgachev
published in: Mathematische Annalen
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164019
review text: Let F be an Enriques surface over an algebraically closed field of characteristic \(p\geq 0\) embedded into a projective space as a surface of degree d. The main result of this paper asserts that the set of smooth rational curves on F is either empty or contains a curve of degree \(\leq d\). One of immediate corollaries of this result is the fact that polarized Enriques surfaces without smooth rational curves on them are parametrized by a constructible subset of the Hilbert scheme. By a finer argument we prove that this subset is open dense, if \(p\neq 2\). - The main technical tool of this paper is the arithmetic of the Picard lattice of F, an integral even unimodular quadratic form of rank 10 and signature (1,9).
Mathematics Subject Classification ID: 14H45
Mathematics Subject Classification ID: 14J25
Mathematics Subject Classification ID: 14M20
zbMATH DE Number: 3867499
zbMATH Keywords: smooth rational curves on Enriques surface
zbMATH Keywords: characteristic p
zbMATH Keywords: arithmetic of the Picard lattice
MaRDI profile type: Publication
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OpenAlex ID: W1977366873
description: scientific article; zbMATH DE number 3867499