Birational invariance in logarithmic Gromov–Witten theory
By D. Abramovich, Jonathan Wise. Compositio Mathematica, 2013
82 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4511e9ce770b5f6b9357d2c43135f7e6ed850ab9
How researchers see this paper
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In Geometry and Topology
- Dhruv Ranganathan
- D. Abramovich
- Martin Ulirsch
- Jonathan Wise
- Mark Gross
- Qile Chen
- Bernd S Siebert
- David Jensen
In Mathematical Physics
- Dhruv Ranganathan
- Mark Gross
- Bernd S Siebert
- D. Abramovich
- David Jensen
- Jonathan Wise
- Qile Chen
- Martin Ulirsch
Citations in the corpus
- Logarithmic Gromov–Witten theory with expansions (2019, methodology): “In light of advances in logarithmically étale descent, this is largely an expositional choice [6, 10].”
- A MODULI STACK OF TROPICAL CURVES (2017, result): “mplex by evaluating the functor of points of the tropicalization on the commutative monoid R≥0 ∪{∞} (see Section 5.5 for details). 5 Tropicalization via Artinfans. ThetheoryofArtinfans was developedin[AW18] and [ACMW17] (see also [ACM+16a] and [Uli19]) as an incarnation of cone stacks in the categor”
- Decomposition of degenerate Gromov–Witten invariants (2017, methodology): “irst, we will choose a logarithmic modification h: X˜ → X. The modification his chosen to accommodate a situation at hand — in our applications the datum of a rigid tropical map. Given a modification h, [AW] constructed a morphism M(h) : M(X/B˜ ) → M(X/B) of moduli stacks of basic stable logarithmic ma”
- Brill-Noether theory for curves of a fixed gonality (2017, methodology): “Given a proper toric varietyZ , work of [2, 5, 29] produces moduli spaces L (Z) and L (AZ) of logarithmic prestable maps to Z and AZ respectively.”