… We call \(\mathsf {N}_{n, (\beta ,d)}^{X}\) the reduced Pandharipande–Thomas or stable
pair invariants of X. Theorem 1 is the following analog of (1) for the reduced theory: …

… We explicitly compute refined invariants in low degree for local P2 and local P1 × P1 and
check that they agree with the predictions of the direct integration of the generalized …

… stable pairs are scheme theoretically supported on the zero section, we express stable pair
invariants … verifications for these local geometries for more general low degree curve classes. …

… of stable pair invariants. In the first section we introduce the notion of a stable pair … This
neighborhood U must be equal to X × B: we can reduce this to the affine case, so assume X = …

… These invariants are automatically zero unless L ⋅ β = 0 by … stable pair invariants in terms
of Gopakumar-Vafa invariants of D … By Grothendieck-Riemann-Roch formula, we reduce the …

… stable pair invariants to the Poincaré invariants of Dürr–Kabanov–Okonek. The latter are equal
to the Seiberg–Witten invariants of |… Reduced stable pair invariants have been studied by …

… for stable pairs on the P2-bundle. The branch maps of Thaddeus and Alexeev-Knutsen [1]
are reduced … Since the stable pair invariants Pn,β are certainly integral, we conclude the BPS …

… Invariants counting curves in X via stable pairs have been defined in [26]. A … For the
application to reduced β, we only need the result for stable pairs with reduced support. So, we work …

… Since the reduced stable pair invariants are still defined for S, β … Although stable pair invariants
in classes β, k−β generally … We also study the non-reduced stable pair invariants of any S…

… For a K3 surface S and a class β ∈ Pic(S), we study motivic invariants of stable pairs moduli
… reduced virtual fundamental class of the moduli space of stable maps to S or the stable pairs …