Scattering diagrams, stability conditions, and coherent sheaves on ℙ²

DOI10.1090/jag/795zbMath1502.14137arXiv1909.02985OpenAlexW4283371046MaRDI QIDQ5094674

Pierrick Bousseau

Publication date: 4 August 2022

Published in: Journal of Algebraic Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.02985

zbMATH Keywords

stability conditionsscattering diagramssemistable coherent sheaves

Mathematics Subject Classification ID

Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35) Mirror symmetry (algebro-geometric aspects) (14J33) Derived categories of sheaves, dg categories, and related constructions in algebraic geometry (14F08)

Related Items (9)

Tropical correspondence for smooth del Pezzo log Calabi-Yau pairs ⋮ Perverse filtrations, Chern filtrations, and refined BPS invariants for local \(\mathbb{P}^2\) ⋮ Sheaves on non-reduced curves in a projective surface ⋮ Cohomological -dependence of ring structure for the moduli of one-dimensional sheaves on ⋮ Quiver symmetries and wall-crossing invariance ⋮ Cohomological \(\chi\)-independence for moduli of one-dimensional sheaves and moduli of Higgs bundles ⋮ On the log–local principle for the toric boundary ⋮ Some Betti numbers of the moduli of 1-dimensional sheaves on \(\mathbb{P}^2\) ⋮ A proof of N. Takahashi's conjecture for \(( \mathbb{P}^2, E)\) and a refined sheaves/Gromov-Witten correspondence

Cites Work

• Unnamed Item
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• Moduli spaces of \(\alpha\)-stable pairs and wall-crossing on \(\mathbb{P}^2\)
• Minkowski polynomials and mutations
• On the moduli spaces of semi-stable plane sheaves of dimension one and multiplicity five
• Spectral networks
• The classification of semistable plane sheaves supported on sextic curves
• Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants
• Interpolation, Bridgeland stability and monomial schemes in the plane
• The birational geometry of moduli spaces of sheaves on the projective plane
• On the geometry of the moduli spaces of semi-stable sheaves supported on plane quartics
• Derived equivalences from mutations of quivers with potential
• The space of stability conditions on the local projective plane
• An introduction to motivic Hall algebras
• The Betti numbers of the moduli space of stable sheaves of rank 3 on \({\mathbb{P}^2}\)
• From real affine geometry to complex geometry
• Birational models of moduli spaces of coherent sheaves on the projective plane
• Intersection homology. II
• Integral generators for the cohomology ring of moduli spaces of sheaves over Poisson surfaces
• Configurations in abelian categories. II: Ringel-Hall algebras
• The tropical vertex
• Moduli of Bridgeland semistable objects on \(\mathbb{P}^2\)
• Fibrés exceptionnels et suite spectrale de Beilinson généralisée sur \({\mathbb{P}}_ 2({\mathbb{C}})\)
• Exceptional vector bundles on projective spaces
• Intersection homology theory
• Geometric realizations of BPS states in \(N=2\) theories
• Intersection cohomology of moduli spaces of sheaves on surfaces
• Sheaves on \(\mathbb{P}^2\) and generalized Appell functions
• Exponential networks and representations of quivers
• Tropical refined curve counting from higher genera and lambda classes
• Genus zero Gopakumar-Vafa type invariants for Calabi-Yau 4-folds
• The Betti numbers of the moduli space of stable sheaves of rank 2 on a ruled surface
• Mirror symmetry is \(T\)-duality
• Bridgeland-stable moduli spaces for \(K\)-trivial surfaces
• The minimal model program for the Hilbert scheme of points on \(\mathbb P^2\) and Bridgeland stability
• Direct integration for general \(\Omega\) backgrounds
• Exceptional bundles associated to degenerations of surfaces
• The quantum tropical vertex
• Torus action on the moduli spaces of torsion plane sheaves of multiplicity four
• Donaldson-Thomas invariants from tropical disks
• Donaldson-Thomas invariants versus intersection cohomology of quiver moduli
• The geometry of the moduli space of one-dimensional sheaves
• Moduli spaces of semistable sheaves of dimension \(1\) on \(\mathbb{P}^2\)
• BPS invariants of semi-stable sheaves on rational surfaces
• Stability conditions and curve counting invariants on Calabi-Yau 3-folds
• Configurations in abelian categories. IV: Invariants and changing stability conditions
• Stability conditions on curves
• Stability conditions on \(K3\) surfaces
• Stability conditions on triangulated categories
• Théorie de Hodge. II. (Hodge theory. II)
• Théorie de Hodge. III
• The effective cone of the moduli space of sheaves on the plane
• Smoothness and Poisson structures of Bridgeland moduli spaces on Poisson surfaces
• Attractor flow trees, BPS indices and quivers
• Effective divisors on the Hilbert scheme of points in the plane and interpolation for stable bundles
• A theory of generalized Donaldson–Thomas invariants
• Duality, Bridgeland wall-crossing and flips of secant varieties
• The ample cone of moduli spaces of sheaves on the plane
• The decomposition theorem, perverse sheaves and the topology of algebraic maps
• Fibrés stables et fibrés exceptionnels sur $\mathbb{P}_2$
• Fibrés exceptionnels et variétés de modules de faisceaux semi-stables sur P2 ( C ).
• THE MARKOV NUMBERS AND EXCEPTIONAL BUNDLES ON P²
• The Betti numbers of the moduli space of stable sheaves of rank2 on P2.
• MODULI OF REPRESENTATIONS OF FINITE DIMENSIONAL ALGEBRAS
• Scattering diagrams, Hall algebras and stability conditions
• The minimal model program for deformations of Hilbert schemes of points on the projective plane
• Holomorphic anomaly equation for and the Nekrasov-Shatashvili limit of local
• Tropical correspondence for smooth del Pezzo log Calabi-Yau pairs
• The tropical superpotential for $\mathbb{P}^2$
• Log BPS numbers of log Calabi-Yau surfaces
• Wall-Crossing Structures in Donaldson–Thomas Invariants, Integrable Systems and Mirror Symmetry
• THE HOMOLOGY GROUPS OF CERTAIN MODULI SPACES OF PLANE SHEAVES
• MOTIVIC INVARIANTS OF ARTIN STACKS AND 'STACK FUNCTIONS'
• Mixed Hodge modules
• Supergravity flows and D-brane stability
• Log mirror symmetry and local mirror symmetry.

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