相关论文: Stable pairs with descendents on local surfaces I:…

We prove the rationality of the descendent partition function for stable pairs on nonsingular toric 3-folds. The method uses a geometric reduction of the 2- and 3-leg descendent vertices to the 1-leg case. As a consequence, we prove the…

The stable pairs theory of local curves in 3-folds (equivariant with respect to the scaling 2-torus) is studied with stationary descendent insertions. Reduction rules are found to lower descendents when higher than the degree. Factorization…

This paper concerns the recent Virasoro conjecture for the theory of stable pairs on a 3-fold proposed by Oblomkov, Okounkov, Pandharipande and the author in arXiv:2008.12514. Here we extend the conjecture to 3-folds with…

In 2008, Klemm-Pandharipande defined Gopakumar-Vafa type invariants of a Calabi-Yau 4-fold $X$ using Gromov-Witten theory. Recently, Cao-Maulik-Toda proposed a conjectural description of these invariants in terms of stable pair theory. When…

The theory of stable pairs in the derived category yields an enumerative geometry of curves in 3-folds. We evaluate the equivariant vertex for stable pairs on toric 3-folds in terms of weighted box counting. In the toric Calabi-Yau case,…

We define and compute higher rank analogs of Pandharipande-Thomas stable pair invariants in primitive classes for K3 surfaces. Higher rank stable pair invariants for Calabi-Yau threefolds have been defined by Sheshmani \cite{shesh1,shesh2}…

We study the stable pairs theory of local curves in 3-folds with descendent insertions. The rationality of the partition function of descendent invariants is established for the full local curve geometry (equivariant with respect to the…

We survey here the construction and the basic properties of descendent invariants in the theory of stable pairs on nonsingular projective 3-folds. The main topics covered are the rationality of the generating series, the functional…

We prove a formula which relates Euler characteristic of moduli spaces of stable pairs on local K3 surfaces to counting invariants of semistable sheaves on them. Our formula generalizes Kawai-Yoshioka's formula for stable pairs with…

We calculate the stable pair theory of a projective surface $S$. For fixed curve class $\beta\in H^2(S)$ the results are entirely topological, depending on $\beta^2$, $\beta.c_1(S)$, $c_1(S)^2$, $c_2(S)$, $b_1(S)$ \emph{and} invariants of…

We study the moduli spaces of surface pairs $(X,D)$ admitting a log Calabi--Yau fibration $(X,D) \to C$. We develop a series of results on stable reduction and apply them to give an explicit description of the boundary of the KSBA…

We construct a fully equivariant correspondence between Gromov-Witten and stable pairs descendent theories for toric 3-folds X. Our method uses geometric constraints on descendents, A_n surfaces, and the topological vertex. The rationality…

This is the first part in a series of papers on counting surfaces on Calabi-Yau 4-folds. Besides the Hilbert scheme of 2-dimensional subschemes, we introduce \emph{two} types of moduli spaces of stable pairs. We show that all three moduli…

Let S be a nonsingular projective K3 surface. Motivated by the study of the Gromov-Witten theory of the Hilbert scheme of points of S, we conjecture a formula for the Gromov-Witten theory (in all curve classes) of the Calabi-Yau 3-fold S x…

Let $S$ be a smooth projective variety and $\Delta$ a simple normal crossing $\mathbb{Q}$-divisor with coefficients in $(0,1]$. For any ample $\mathbb{Q}$-line bundle $L$ over $S$, we denote by $\mathscr{E}(L)$ the extension sheaf of the…

We relate Pandharipande-Thomas stable pair invariants on Calabi-Yau 3-folds containing the projective plane with those on the derived equivalent orbifolds via wall-crossing method. The difference is described by generalized Donaldson-Thomas…

We consider the moduli space of log smooth pairs formed by a cubic surface and an anticanonical divisor. We describe all compactifications of this moduli space which are constructed using Geometric Invariant Theory and the anticanonical…

In arXiv:2011.08830 we established a series of correspondences relating five enumerative theories of log Calabi-Yau surfaces, i.e. pairs $(Y,D)$ with $Y$ a smooth projective complex surface and $D=D_1+\dots +D_l$ an anticanonical divisor on…

We use the Gromov-Witten/Pairs descendent correspondence for toric 3-folds and degeneration arguments to establish the GW/P correspondence for several compact Calabi-Yau 3-folds (including all CY complete intersections in products of…

The conjectural equivalence of curve counting on Calabi-Yau 3-folds via stable maps and stable pairs is discussed. By considering Calabi-Yau 3-folds with K3 fibrations, the correspondence naturally connects curve and sheaf counting on K3…