Pseudolattices, del pezzo surfaces, and lefschetz fibrations

Andrew Harder, Alan Thompson

Research output: Contribution to journalArticle

Abstract

Motivated by the relationship between numerical Grothendieck groups induced by the embedding of a smooth anticanonical elliptic curve into a del Pezzo surface, we define the notion of a quasi-del Pezzo homomorphism between pseudolattices and establish its basic properties. The primary aim of the paper is then to prove a classification theorem for quasi-del Pezzo homomorphisms, using a pseudolattice variant of the minimal model program. Finally, this result is applied to the classification of a certain class of genus 1 Lefschetz fibrations over discs.

Original languageEnglish (US)
Pages (from-to)2071-2104
Number of pages34
JournalTransactions of the American Mathematical Society
Volume373
Issue number3
DOIs
StatePublished - Jan 1 2020

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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