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Pseudolattices, del Pezzo surfaces, and Lefschetz fibrations

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journal contribution
posted on 06.08.2019 by Andrew Harder, Alan Thompson
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 one Lefschetz fibrations over discs.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Transactions of the American Mathematical Society

Volume

373

Issue

3

Pages

2071 - 2104

Publisher

American Mathematical Society

Version

AM (Accepted Manuscript)

Rights holder

© American Mathematical Society

Publisher statement

First published in Transactions of the American Mathematical Society 373 (March 2020), published by the American Mathematical Society. © 2019 American Mathematical Society.

Acceptance date

29/07/2019

Publication date

2019-09-25

Copyright date

2019

ISSN

0002-9947

eISSN

1088-6850

Language

en

Depositor

Dr Alan Thompson

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