Log canonical models of elliptic surfaces

Kenneth Ascher, Dori Bejleri

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We classify the log canonical models of elliptic surface pairs (f:X→C,S+FA) where f:X→C is an elliptic fibration, S is a section, and FA is a weighted sum of marked fibers. In particular, we show how the log canonical models depend on the choice of the weights. We describe a wall and chamber decomposition of the space of weights based on how the log canonical model changes. In addition, we give a generalized formula for the canonical bundle of an elliptic surface with section and marked fibers. This is the first step in constructing compactifications of moduli spaces of elliptic surfaces using the minimal model program.

Original languageEnglish (US)
Pages (from-to)210-243
Number of pages34
JournalAdvances in Mathematics
Volume320
DOIs
StatePublished - Nov 7 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Birational geometry
  • Elliptic surfaces
  • Log minimal model program (MMP)

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