This is the sequel to the paper [23]. In this paper, we construct the virtual moduli cycles of the
degeneration of the moduli of stable morphisms constructed in [23]. We also construct the …

Given a holomorphic vector bundle E over a compact Kähler manifold X, one defines twisted
Gromov-Witten invariants of X to be intersection numbers in moduli spaces of stable maps f …

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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 construct a localized Gysin …

Given a vector bundle F on a smooth Deligne–Mumford stack X and an invertible
multiplicative characteristic class c, we define orbifold Gromov–Witten invariants of X twisted …

We propose a generalization of Gysin maps for DM-type morphisms of stacks $ F\to G $ that
admit a perfect relative obstruction theory $ E_ {F/G}^{\bullet} $, which we call a" virtual pull …

Abstract Twisted Gromov-Witten invariants are intersection numbers in moduli spaces of
stable maps to a manifold or orbifold X which depend in addition on a vector bundle over X …

Abstract For a Landau–Ginzburg space (C^ n/G, W)(C n/G, W), we construct Witten's top
Chern class as an algebraic cycle using cosection localized virtual cycles in the case where …

We extend to orbifolds the quasimap theory of Ciocan-Fontanine and Kim (Adv Math 225 (6):
3022–3051, 2010; J Geom Phys 75: 17–47, 2014) as well as the genus zero wall-crossing …

We introduce a variant of stable logarithmic maps, which we call punctured logarithmic
maps. They allow an extension of logarithmic Gromov-Witten theory in which marked points …