Log geometry and exploded manifolds

Brett Parker

doi:10.1007/s12188-012-0065-8

Log geometry and exploded manifolds

Brett Parker^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 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 language	English
Pages (from-to)	43-81
Number of pages	39
Journal	Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
Volume	82
Issue number	1
DOIs	https://doi.org/10.1007/s12188-012-0065-8
Publication status	Published - Apr 2012

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10.1007/s12188-012-0065-8

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title = "Log geometry and exploded manifolds",

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.",

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AB - 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.

KW - Exploded manifolds

KW - Gromov-Witten invariants

KW - Log geometry

KW - Tropical geometry

UR - https://www.scopus.com/pages/publications/84861227308

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DO - 10.1007/s12188-012-0065-8

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JO - Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg

JF - Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg

IS - 1

ER -

Log geometry and exploded manifolds

Abstract

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