Higher genus Gromov–Witten invariants as genus zero invariants of symmetric products

Costello, Kevin

doi:10.4007/annals.2006.164.561

Cited by 71 publications

(82 citation statements)

References 30 publications

(55 reference statements)

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“…Our Lemma 3.6 is a slight generalization of Lai's results. The relative version of the (strong) virtual push-forward theorem is a generalization of Costello's push-forward formula for virtual cycles [4]. The applications of these results generalize several previous results as follows.…”

Section: Introductionsupporting

confidence: 63%

“…The strong virtual push-forward property is a consequence of the push forward property, the properties of virtual pull-backs for algebraic equivalence classes and the conservation of number principle. The relative version of the strong virtual push-forward property (Proposition 3.14) is a generalization of Costello's virtual push-forward property in [4].…”

Section: Introductionmentioning

confidence: 99%

“…We will take this semigroup to be H 2 .X /, for some smooth variety X . In [4] it is shown that the forgetful map M g;n;ˇ! M g;n is étale and that the natural forgetful map…”

mentioning

confidence: 99%

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Virtual push-forwards

Manolache

2012

Geom. Topol.

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Let pW F ! G be a morphism of DM stacks of positive virtual relative dimension k and let 2 A k .F /. We give sufficient conditions for p . OEF virt / to be a multiple of OEG virt . We show an analogue of the conservation of number for virtually smooth families. We show implications to Gromov-Witten invariants and give a new proof of a theorem of Marian, Oprea and Pandharipande [19] which compares the virtual classes of moduli spaces of stable maps and moduli spaces of stable quotients.

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Section: Introductionsupporting

confidence: 63%

Section: Introductionmentioning

confidence: 99%

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Virtual push-forwards

Manolache

2012

Geom. Topol.

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“…We will make the observation that one variant of the moduli space introduced by Kim can be identified with the virtual normalization of the space of maps constructed by Kim, Kresch, and Oh. This will let us apply K. Costello's Theorem 5.0.1 in [3].…”

Section: Introductionmentioning

confidence: 99%

Virtual normalization and virtual fundamental classes

Martín

2011

Proc. Amer. Math. Soc.

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“…Proof. From Costello's push forward formula [10] applied to the cartesian diagram M Q g,n (G(k, r), d)…”

Section: Proof Let Us Considermentioning

confidence: 99%

Stable maps and stable quotients

Manolache¹

2014

Compositio Math.

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We analyze the relationship between two compactifications of the moduli space of maps from curves to a Grassmannian: the Kontsevich moduli space of stable maps and the Marian-Oprea-Pandharipande moduli space of stable quotients. We construct a moduli space which dominates both the moduli space of stable maps to a Grassmannian and the moduli space of stable quotients, and equip our moduli space with a virtual fundamental class. We relate the virtual fundamental classes of all three moduli spaces using the virtual push-forward formula. This gives a new proof of a theorem of Marian-OpreaPandharipande: that enumerative invariants defined as intersection numbers in the stable quotient moduli space coincide with GromovWitten invariants.

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Higher genus Gromov–Witten invariants as genus zero invariants of symmetric products

Cited by 71 publications

References 30 publications

Virtual push-forwards

Virtual push-forwards

Virtual normalization and virtual fundamental classes

Stable maps and stable quotients

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