Homological projective duality

DOI10.1007/s10240-007-0006-8zbMath1131.14017arXivmath/0507292OpenAlexW2073163485MaRDI QIDQ2465552

Alexander G. Kuznetsov

Publication date: 4 January 2008

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0507292

zbMATH Keywords

hyperplane sectionsprojective dualityderived categories of singularities

Mathematics Subject Classification ID

Related Items (86)

Decompositions of moduli spaces of vector bundles and graph potentials ⋮ Calabi-Yau 3-folds from projective joins of del Pezzo manifolds ⋮ Homological projective duality for determinantal varieties ⋮ ON THE CHOW THEORY OF PROJECTIVIZATIONS ⋮ Derived Categories View on Rationality Problems ⋮ Derived equivalent Calabi-Yau threefolds from cubic fourfolds ⋮ Spectral sequences and vacua in \( \mathcal{N}=2 \) gauged linear quantum mechanics with potentials ⋮ Derived Categories of Families of Sextic del Pezzo Surfaces ⋮ A GLSM view on homological projective duality ⋮ The integral Hodge conjecture for two-dimensional Calabi–Yau categories ⋮ On the motive of codimension 2 linear sections of \(\operatorname{Gr}(3,6)\) ⋮ GLSMs for exotic Grassmannians ⋮ Fourier--Mukai transforms for Gorenstein schemes ⋮ Derived categories of Artin-Mumford double solids ⋮ A refined derived Torelli theorem for Enriques surfaces ⋮ Non-commutative resolutions of quotient singularities for reductive groups ⋮ Perverse schobers and birational geometry ⋮ On linear sections of the spinor tenfold. I ⋮ Predictions for Gromov-Witten invariants of noncommutative resolutions ⋮ On stringy Euler characteristics of Clifford non-commutative varieties ⋮ HPD-invariance of the Tate conjecture(s) ⋮ Noncommutative Hodge conjecture ⋮ Serre functors of residual categories via hybrid models ⋮ Semiorthogonal decomposition via categorical action ⋮ Derived categories of flips and cubic hypersurfaces ⋮ Noncommutative homological projective duality ⋮ Frobenius and spherical codomains and neighbourhoods ⋮ On quantum cohomology of Grassmannians of isotropic lines, unfoldings of $A_n$-singularities, and Lefschetz exceptional collections ⋮ Kuznetsov's Fano threefold conjecture via \(K3\) categories and enhanced group actions ⋮ Topological strings on non-commutative resolutions ⋮ Two-dimensional gauge dynamics and the topology of singular determinantal varieties ⋮ Derived categories of hearts on Kuznetsov components ⋮ Duality related with key varieties of \(\mathbb{Q} \)-Fano threefolds constructed from projective bundles ⋮ Categorical cones and quadratic homological projective duality ⋮ Categorical Torelli theorems: results and open problems ⋮ Derived categories of the Cayley plane and the coadjoint Grassmannian of type F ⋮ Semiorthogonal decompositions in families ⋮ Noncommutative crepant resolutions, an overview ⋮ On the derived category of ⋮ Floer cohomology and pencils of quadrics ⋮ A categorical invariant for cubic threefolds ⋮ Fibrations in complete intersections of quadrics, Clifford algebras, derived categories, and rationality problems ⋮ Derived categories of quadric fibrations and intersections of quadrics ⋮ Lectures on Non-commutative K3 Surfaces, Bridgeland Stability, and Moduli Spaces ⋮ Base change for semiorthogonal decompositions ⋮ Some remarks concerning Voevodsky's nilpotence conjecture ⋮ Dual pairs of gauged linear sigma models and derived equivalences of Calabi-Yau threefolds ⋮ Movable vs monodromy nilpotent cones of Calabi-Yau manifolds ⋮ On the derived categories of degree \(d\) hypersurface fibrations ⋮ Homological projective duality via variation of geometric invariant theory quotients ⋮ GLSMs for partial flag manifolds ⋮ Fano manifolds of Calabi-Yau Hodge type ⋮ ABEL–JACOBI MAPS FOR HYPERSURFACES AND NONCOMMUTATIVE CALABI–YAU'S ⋮ On the derived category of the Cayley plane ⋮ Comparing the commutative and non-commutative resolutions for determinantal varieties of skew symmetric and symmetric matrices ⋮ Towards homological projective duality for \(\mathsf{S}^2 \mathbb{P}^3\) and \(\mathsf{S}^2 \mathbb{P}^4\) ⋮ Derived categories of Gushel–Mukai varieties ⋮ Grothendieck ring of varieties, D- and L-equivalence, and families of quadrics ⋮ Recent developments on noncommutative motives ⋮ Categorical Plücker formula and homological projective duality ⋮ Quintic threefolds and Fano elevenfolds ⋮ On the derived category of the Cayley Grassmannian ⋮ Duality in two-dimensional \((2,2)\) supersymmetric non-abelian gauge theories ⋮ The homological projective dual of ⋮ Embedding derived categories of Enriques surfaces in derived categories of Fano varieties ⋮ Lefschetz exceptional collections in \(S_k\)-equivariant categories of \((\mathbb{P}^n)^k\) ⋮ Intersections of two Grassmannians in \(\mathbb{P}^9\) ⋮ GLSMs, joins, and nonperturbatively-realized geometries ⋮ Derived equivalent Hilbert schemes of points on \(K3\) surfaces which are not birational ⋮ Noncommutative Riemann hypothesis ⋮ Obstructions to semiorthogonal decompositions for singular threefolds I: K-theory ⋮ Calabi-Yau and fractional Calabi-Yau categories ⋮ Derived categories of projectivizations and flops ⋮ Cycles, derived categories, and rationality ⋮ A note on Grothendieck’s standard conjectures of type 𝐶⁺ and 𝐷 in positive characteristic ⋮ A-twisted Landau-Ginzburg models ⋮ On the derived category of the Cayley plane II ⋮ Hori-mological projective duality ⋮ Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges ⋮ Homological projective duality for quadrics ⋮ A note on Grothendieck’s standard conjectures of type $C^+$ and $D$ ⋮ Categorical joins ⋮ Hybrid models for homological projective duals and noncommutative resolutions ⋮ Minimal Lefschetz decompositions of the derived categories for Grassmannians ⋮ A refined derived Torelli theorem for Enriques surfaces. II: The non-generic case ⋮ Simultaneous categorical resolutions

Cites Work

• Equivalences of derived categories and \(K3\) surfaces
• Reconstruction of a variety from the derived category and groups of autoequivalences
• Triangulated categories of singularities and equivalences between Landau-Ginzburg models
• Homological Algebra of Mirror Symmetry
• Hyperplane sections and derived categories
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Homological projective duality