Virtual fundamental classes of zero loci

A mirror theorem for the mirror quintic

“…A proof can be found in e.g. [10]. (That proof, given in the nonorbifold setting there, can be readily modified to the orbifold setting.)…”

Quantum Lefschetz hyperplane theorem

“…(from different approaches) that some suitable correlators on P r d actually produce the desired hypergeometric series. However, neither G 0,0 (P r , d) nor P r d is the right space to perform the integral (6). The way to resolve this issue was to identify M 0,1 (P r , d) as a fixed point component of C * -action on G 0,0 (P r , d).…”

Functoriality in intersection theory and a conjecture of Cox, Katz, and Lee

“…A recent paper by Cox et al [3] states the following conjecture on virtual moduli cycles. Let X be a nonsingular complex projective variety; a vector bundle V on X is convex if, for every genus zero stable map ϕ : C → X, we have H 1 (C, f * V ) = 0.…”

“…Conjecture (Cox et al [3]). Fix X and n, and let V be a convex vector bundle on X. Denote by i : Y → X the inclusion defined by the zero locus of a regular section of V , and for γ ∈ H 2 (Y, Z), denote by j γ the natural inclusionM 0,n (Y, γ) →M 0,n (X, i * γ).…”