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Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties

· 1996 · alg-geom · arXiv alg-geom/9602007

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abstract

We introduce a method of constructing the virtual cycle of any scheme associated with a tangent-obstruction complex. We apply this method to constructing the virtual moduli cycle of the moduli of stable maps from n-pointed genus g curves to any smooth projective variety. As an application, we give an algebraic definition of GW-invariants for any smooth projective variety.

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Virtual Jeffrey--Kirwan localisation

math.AG · 2026-07-06 · accept · novelty 7.0

Virtual integrals over GIT quotients X//G equal Jeffrey–Kirwan residues of virtual integrals over T-fixed loci, for perfect obstruction theories and oriented (−2)-shifted symplectic structures, in cohomology and K-theory.

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  • Virtual Jeffrey--Kirwan localisation math.AG · 2026-07-06 · accept · none · ref 35 · internal anchor

    Virtual integrals over GIT quotients X//G equal Jeffrey–Kirwan residues of virtual integrals over T-fixed loci, for perfect obstruction theories and oriented (−2)-shifted symplectic structures, in cohomology and K-theory.