42 citations · 212 across the 25 of their papers we have counts for
22 papers · 1 filter
Log Calabi-Yau compactifications of character varieties
Hülya Argüz, Pierrick Bousseau
We prove that the character varieties of compact oriented surfaces and the generic relative character varieties of punctured surfaces admit di…
Geometric helices on del Pezzo surfaces from tilting
Pierrick Bousseau
We prove that all geometric helices in the derived category of coherent sheaves on a del Pezzo surface are related by a sequence of elementary operations: rotation, shifting, ortho…
BPS polynomials and Welschinger invariants
Hülya Argüz, Pierrick Bousseau
We generalize Block-Göttsche polynomials, originally defined for toric del Pezzo surfaces, to arbitrary surfaces. To do this, we show that these polynomials arise as special cases…
The KSBA moduli space of stable log Calabi-Yau surfaces
Valery Alexeev, Hülya Argüz, Pierrick Bousseau
We prove that every irreducible component of the coarse Kollár-Shepherd-Barron and Alexeev (KSBA) moduli space of stable log Calabi--Yau surfaces admits a finite cover by a project…
Quivers and curves in higher dimension
Hülya Argüz, Pierrick Bousseau
We prove a correspondence between Donaldson-Thomas invariants of quivers with potential having trivial attractor invariants and genus zero punctured Gromov-Witten invariants of hol…
All-genus WDVV recursion, quivers, and BPS invariants
Pierrick Bousseau, Longting Wu
Let be a smooth projective surface and a smooth rational ample divisor in . We prove an all-genus generalization of the genus WDVV equation for primary Gromov--Witte…
Quivers, Flow Trees, and Log Curves
Hülya Argüz, Pierrick Bousseau
Donaldson-Thomas (DT) invariants of a quiver with potential can be expressed in terms of simpler attractor DT invariants by a universal formula. The coefficients in this formula ar…
Fock-Goncharov dual cluster varieties and Gross-Siebert mirrors
Hülya Argüz, Pierrick Bousseau
Cluster varieties come in pairs: for any cluster variety there is an associated Fock-Goncharov dual cluster variety. On the other hand, in the context o…
Gromov-Witten Theory of Complete Intersections via Nodal Invariants
Hülya Argüz, Pierrick Bousseau, Rahul Pandharipande +1
We provide an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. We also prove…
Stable maps to Looijenga pairs: orbifold examples
Pierrick Bousseau, Andrea Brini, Michel van Garrel
In arXiv:2011.08830 we established a series of correspondences relating five enumerative theories of log Calabi-Yau surfaces, i.e. pairs with a smooth projective comple…
Stable maps to Looijenga pairs
Pierrick Bousseau, Andrea Brini, Michel van Garrel
A log Calabi-Yau surface with maximal boundary, or Looijenga pair, is a pair with a smooth rational projective complex surface and an ant…
Real Log Curves in Toric Varieties, Tropical Curves, and Log Welschinger Invariants
Hülya Argüz, Pierrick Bousseau
We give a tropical description of the counting of real log curves in toric degenerations of toric varieties. We treat the case of genus zero curves and all non-superabundant higher…
Scattering diagrams, sheaves, and curves
Pierrick Bousseau
We review the recent proof of the N.Takahashi's conjecture on genus Gromov-Witten invariants of , where is a smooth cubic curve in the complex projective…
Holomorphic anomaly equation for and the Nekrasov-Shatashvili limit of local
Pierrick Bousseau, Honglu Fan, Shuai Guo +1
We prove a higher genus version of the genus local-relative correspondence of van Garrel-Graber-Ruddat: for a pair with a smooth projective variety and a nef sm…
A proof of N.Takahashi's conjecture for and a refined sheaves/Gromov-Witten correspondence
Pierrick Bousseau
We prove N.Takahashi's conjecture determining the contribution of each contact point in genus- maximal contact Gromov-Witten theory of relative to a smooth cubic…
Scattering diagrams, stability conditions, and coherent sheaves on
Pierrick Bousseau
We show that a purely algebraic structure, a two-dimensional scattering diagram, describes a large part of the wall-crossing behavior of moduli spaces of Bridgeland semistable obje…
On the log-local principle for the toric boundary
Pierrick Bousseau, Andrea Brini, Michel van Garrel
Let be a smooth projective complex variety and let be a reduced normal crossing divisor on with each component smooth, irreducible, and nef. The lo…
Refined floor diagrams from higher genera and lambda classes
Pierrick Bousseau
We show that, after the change of variables , refined floor diagrams for and Hirzebruch surfaces compute generating series of higher genus relative Gromov-…
On an example of quiver DT/relative GW correspondence
Pierrick Bousseau
We explain and generalize a recent result of Reineke-Weist by showing how to reduce it to the Gromov-Witten/Kronecker correspondence by a degeneration and blow-up. We also refine t…
Quantum mirrors of log Calabi-Yau surfaces and higher genus curve counting
Pierrick Bousseau
Gross, Hacking, and Keel have constructed mirrors of log Calabi-Yau surfaces in terms of counts of rational curves. Using -deformed scattering diagrams defined in terms of highe…
The quantum tropical vertex
Pierrick Bousseau
Gross-Pandharipande-Siebert have shown that the 2-dimensional Kontsevich-Soibelman scattering diagrams compute certain genus zero log Gromov-Witten invariants of log Calabi-Yau sur…
Tropical refined curve counting from higher genera and lambda classes
Pierrick Bousseau
Block and Göttsche have defined a -number refinement of counts of tropical curves in . Under the change of variables , we show that the result is a gener…