Moduli of weighted stable elliptic surfaces and invariance of log plurigenera

Kenneth Ascher, Dori Bejleri

Research output: Contribution to journalArticlepeer-review

Abstract

Motivated by Hassett's weighted pointed stable curves, we use the log minimal model program to construct compact moduli spaces parameterizing weighted stable elliptic surfaces — elliptic fibrations with section and marked fibers each weighted between zero and one. Moreover, we show that the domain of weights admits a wall and chamber structure, describe the induced wall-crossing morphisms on the moduli spaces as the weight vector varies, and describe the surfaces that appear on the boundary of the moduli space. The main technical result is a proof of invariance of log plurigenera for slc elliptic surface pairs with arbitrary weights.

Original languageEnglish (US)
Pages (from-to)617-677
Number of pages61
JournalProceedings of the London Mathematical Society
Volume122
Issue number5
DOIs
StatePublished - May 2021

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • 14J10 (primary)
  • 14J27 (secondary)

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