Log geometry and exploded manifolds

Brett Parker

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7 Citations (Scopus)

Abstract

Log Gromov-Witten invariants have recently been defined separately by Gross and Siebert and Abramovich and Chen. This paper provides a dictionary between log geometry and holomorphic exploded manifolds in order to compare Gromov-Witten invariants defined using exploded manifolds or log schemes. The gluing formula for Gromov-Witten invariants of exploded manifolds suggests an approach to proving analogous gluing formulas for log Gromov-Witten invariants.

Original languageEnglish
Pages (from-to)43-81
Number of pages39
JournalAbhandlungen aus dem Mathematischen Seminar der Universität Hamburg
Volume82
Issue number1
DOIs
Publication statusPublished - 1 Apr 2012
Externally publishedYes

Keywords

  • Exploded manifolds
  • Gromov-Witten invariants
  • Log geometry
  • Tropical geometry

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