Localizing virtual cycles by cosections
146 citations recorded by the source corpus.
We show that a cosection of the obstruction sheaf of a perfect obstruction theory localizes the virtual cycle to the non-surjective locus of the cosection. We give algebraic constructions of localized Gysin maps and localized virtual cycles. Various applications of these constructions are discussed.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/944c43ed4b4b6e95617d3e4fea1726650653c590
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Quot schemes of curves and surfaces: virtual classes, integrals, Euler characteristics (2019, background): “By [20], the virtual fundamental cycle is localized along such quotients.”
- Torus localization and wall crossing for cosection localized virtual cycles (2015, methodology): “The construction of [X]vir loc in ([18]) is obtained in two steps: • (cone reduction) the intrinsic normal cone CX has support contained in E(σ) where E(σ) = E|X(σ) ∪ ker(E|U → CU); • (localized Gysin map) there is a cosection localized Gysin map 0E,loc : A∗(E(σ)) −→ A∗(X(σ)) compatible with the usu”
- Curves on K3 surfaces and modular forms (2010, unknown): “rm, Mg(X,ι∗β) admits a reduced obstruction theory and reduced virtual class, [Mg(X,ι∗β)] red ∈ A 1(Mg(X,ι∗β),Q). 10A more detailed account of the deformation theory in [19] has appeared very recently [20]. 12 MAULIK,PANDHARIPANDE,THOMAS,PIXTON The construction of the reduced theory exactly follows S”