General wall crossing formula

Wall-crossing made smooth

In D = 4,N = 2 theories on R, the index receives contributions not only from single-particle BPS states, counted by the BPS indices, but also from multi-particle states made of BPS constituents. In a recent work [1], a general formula expressing the index in terms of the BPS indices was proposed, which is smooth across walls of marginal stability and reproduces the expected single-particle cont...

Wall-crossing Functors

Db(Coh(Aθ λ )) ∼ −→ D(Coh(Aλ)) for two different generic θ, θ′. These derived equivalences will play a crucial role in proving that ImCCv ⊂ Lω[ν]. They were introduced in [BPW, Section 6] under the name of twisting functors. Let us recall from Lecture 3 that abelian localization holds for (λ + nθ, θ) for all n sufficiently large, see Proposition 2.2 there. Also recall that Coh(Aλ) ∼ −→ Coh(Aλ+n...

Paradan’s wall crossing formula for partition functions and Khovanski-Pukhlikov differential operator

A Wall-crossing Formula for Gromov-witten Invariants under Variation of Git Quotient

We prove a quantum version of Kalkman’s wall-crossing formula [37], [44] comparing intersection pairings on geometric invariant theory (git) quotients related by a change in polarization. Each expression in the classical formula is quantized in the sense that it is replaced by an integral over moduli spaces of certain stable maps; in particular, the wall-crossing terms are gauged Gromov-Witten ...

Perverse Coherent Sheaves on Blow-up. Ii. Wall-crossing and Betti Numbers Formula

This is the second of series of papers studyig moduli spaces of a certain class of coherent sheaves, which we call stable perverse coherent sheaves, on the blow-up p : X̂ → X of a projective surface X at a point 0. The followings are main results of this paper: a) We describe the wall-crossing between moduli spaces caused by twisting of the line bundle O(C) associated with the exceptional diviso...