Categorical Plücker Formula and Homological Projective Duality

Abstract

Homological Projective duality (HP-duality) theory, introduced by Kuznetsov [42], is one of the most powerful frameworks in the homological study of algebraic geometry. The main result (HP-duality theorem) of the theory gives complete descriptions of bounded derived categories of coherent sheaves of (dual) linear sections of HP-dual varieties. We show the theorem also holds for more general intersections beyond linear sections. More explicitly, for a given HP-dual pair $(X,Y)$, then analogue of HP-duality theorem holds for their intersections with another HP-dual pair $(S,T)$, provided that they intersect properly. We also prove a relative version of our main result. Taking $(S,T)$ to be dual linear subspaces (resp. subbundles), our method provides a more direct proof of the original (relative) HP-duality theorem.

68 pages, 5 figures

References in corpus (3)

• Phases Of N=2 Theories In 1+1 Dimensions With Boundary
• Hochschild homology and semiorthogonal decompositions
• Non-commutative resolutions of quotient singularities

Cited by in corpus (5)

• On the Chow theory of projectivizations
• Categorical cones and quadratic homological projective duality
• Categorical duality between joins and intersections
• Blowing up linear categories, refinements, and homological projective duality with base locus
• Derived category of projectivization and generalized linear duality