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Birational invariance in logarithmic Gromov–Witten theory

Part of: Algebraic geometry: Foundations Birational geometry Curves Projective and enumerative geometry Families, fibrations

Published online by Cambridge University Press:  29 January 2018

Dan Abramovich  and
Jonathan Wise
Dan Abramovich
Affiliation:
Department of Mathematics, Brown University, Box 1917, Providence, RI 02912, USA email [email protected]
Jonathan Wise
Affiliation:
University of Colorado, Boulder, CO 80309-0395, USA email [email protected]
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Abstract

Gromov–Witten invariants have been constructed to be deformation invariant, but their behavior under other transformations is subtle. We show that logarithmic Gromov–Witten invariants are also invariant under appropriately defined logarithmic modifications.

Keywords

Gromov–Witten theorylogarithmic structuresbirational transformationsstable maps

MSC classification

Primary: 14H10: Families, moduli (algebraic) 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants 14D23: Stacks and moduli problems 14A20: Generalizations (algebraic spaces, stacks) 14E05: Rational and birational maps
Type
Research Article
Information
Compositio Mathematica , Volume 154 , Issue 3 , March 2018 , pp. 595 - 620
Copyright
© The Authors 2018 

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