Embedding pointed curves in K3 surfaces

Brendan Hassett, Yuri Tschinkel

Research output: Contribution to journalArticle

Abstract

We analyze morphisms from pointed curves to K3 surfaces with a distinguished rational curve, such that the marked points are taken to the rational curve, perhaps with specified cross ratios. This builds on work of Mukai and others characterizing embeddings of curves into K3 surfaces via non-abelian Brill–Noether theory. Our study leads naturally to enumerative problems, which we solve in several specific cases. These have applications to the existence of sections of del Pezzo fibrations with prescribed invariants.

Original languageEnglish (US)
Pages (from-to)927-953
Number of pages27
JournalMathematische Zeitschrift
Volume278
Issue number3-4
DOIs
StatePublished - Nov 12 2014

Fingerprint

K3 Surfaces
Rational Curves
Cross ratio
Curve
del operator
Fibration
Morphisms
Invariant

Keywords

  • Brill–Noether theory
  • K3 surfaces

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Embedding pointed curves in K3 surfaces. / Hassett, Brendan; Tschinkel, Yuri.

In: Mathematische Zeitschrift, Vol. 278, No. 3-4, 12.11.2014, p. 927-953.

Research output: Contribution to journalArticle

Hassett, Brendan ; Tschinkel, Yuri. / Embedding pointed curves in K3 surfaces. In: Mathematische Zeitschrift. 2014 ; Vol. 278, No. 3-4. pp. 927-953.
@article{a088cfb8f4514473a4c37d5ea5f3ddba,
title = "Embedding pointed curves in K3 surfaces",
abstract = "We analyze morphisms from pointed curves to K3 surfaces with a distinguished rational curve, such that the marked points are taken to the rational curve, perhaps with specified cross ratios. This builds on work of Mukai and others characterizing embeddings of curves into K3 surfaces via non-abelian Brill–Noether theory. Our study leads naturally to enumerative problems, which we solve in several specific cases. These have applications to the existence of sections of del Pezzo fibrations with prescribed invariants.",
keywords = "Brill–Noether theory, K3 surfaces",
author = "Brendan Hassett and Yuri Tschinkel",
year = "2014",
month = "11",
day = "12",
doi = "10.1007/s00209-014-1339-x",
language = "English (US)",
volume = "278",
pages = "927--953",
journal = "Mathematische Zeitschrift",
issn = "0025-5874",
publisher = "Springer New York",
number = "3-4",

}

TY - JOUR

T1 - Embedding pointed curves in K3 surfaces

AU - Hassett, Brendan

AU - Tschinkel, Yuri

PY - 2014/11/12

Y1 - 2014/11/12

N2 - We analyze morphisms from pointed curves to K3 surfaces with a distinguished rational curve, such that the marked points are taken to the rational curve, perhaps with specified cross ratios. This builds on work of Mukai and others characterizing embeddings of curves into K3 surfaces via non-abelian Brill–Noether theory. Our study leads naturally to enumerative problems, which we solve in several specific cases. These have applications to the existence of sections of del Pezzo fibrations with prescribed invariants.

AB - We analyze morphisms from pointed curves to K3 surfaces with a distinguished rational curve, such that the marked points are taken to the rational curve, perhaps with specified cross ratios. This builds on work of Mukai and others characterizing embeddings of curves into K3 surfaces via non-abelian Brill–Noether theory. Our study leads naturally to enumerative problems, which we solve in several specific cases. These have applications to the existence of sections of del Pezzo fibrations with prescribed invariants.

KW - Brill–Noether theory

KW - K3 surfaces

UR - http://www.scopus.com/inward/record.url?scp=84911968031&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84911968031&partnerID=8YFLogxK

U2 - 10.1007/s00209-014-1339-x

DO - 10.1007/s00209-014-1339-x

M3 - Article

VL - 278

SP - 927

EP - 953

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

SN - 0025-5874

IS - 3-4

ER -