Algebraic orbifold quantum products

Abramovich, Dan; Graber, T.M.; Vistoli, Angelo

doi:10.1090/conm/310/05397

Cited by 129 publications

(285 citation statements)

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“…Gromov-Witten invariants for orbifolds were defined by Chen and Ruan [7], [8], [9] in symplectic topology and Abramovich, Graber, Vistoli [3], [2] in algebraic geometry. Chen and Ruan's work introduced the orbifold cohomology groups H * orb , as the ordinary cohomology of the space of twisted sectors of an orbifold.…”

Section: Orbifold Gromov-witten Theorymentioning

confidence: 99%

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

Costello

2006

Ann. Math.

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Section: Orbifold Gromov-witten Theorymentioning

confidence: 99%

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

Costello

2006

Ann. Math.

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“…Recently orbifold cohomology rings, i.e. a ring structure on the orbifold cohomology have been defined as a special case of quantum cohomology of orbifolds [12], [2], [1]. In [50] it is conjectured for an orbifold X with a hyperkähler resolution Y → X, i.e.…”

Section: Orbifolds and Orbifold Cohomologymentioning

confidence: 99%

On the Motive of the Hilbert scheme of points on a surface

Göttsche

2001

Mathematical Research Letters

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The Hilbert scheme S[n] of points on an algebraic surface S is a simple example of a moduli space and also a nice (crepant) resolution of singularities of the symmetric power S (n) . For many phenomena expected for moduli spaces and nice resolutions of singular varieties it is a model case. Hilbert schemes of points have connections to several fields of mathematics, including moduli spaces of sheaves, Donaldson invariants, enumerative geometry of curves, infinite dimensional Lie algebras and vertex algebras and also to theoretical physics. This talk will try to give an overview over these connections. IntroductionThe Hilbert scheme S[n] of points on a complex projective algebraic surface S is a a parameter variety for finite subschemes of length n on S. It is a nice (crepant) resolution of singularities of the n-fold symmetric power S (n) of S. If S is a K3 surface or an abelian surface, then S[n] is a compact, holomorphic symplectic (thus hyperkähler) manifold. Thus S [n] is at the same time a basic example of a moduli space and an example of a nice resolution of singularities of a singular variety. There are a number of conjectures and general phenomena, many of which originating from theoretical physics, both about moduli spaces for objects on surfaces and about nice resolutions of singularities. In all of these the Hilbert scheme of points can be viewed as a model case and sometimes as the main motivating example. Hilbert schemes of points on a surface have connections to many topics in mathematics, including moduli spaces of sheaves and vector bundles, Donaldson invariants, Gromov-Witten invariants and enumerative geometry of curves, infinite dimensional Lie algebras and vertex algebras, noncommutative geometry and also theoretical physics.

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“…The definition of the orbifold cohomology can be found in [CR04] or in [AGV02]. To prove the theorem above, we only use the fact that the gcd p = 1 and not that the p i 's are well-formed.…”

Section: T T T T T T T T T Cmentioning

confidence: 99%