Blowing up linear categories, refinements, and homological projective duality with base locus
arXiv:1811.05132
Abstract
In this paper, we first introduce geometric operations for linear categories, and as a consequence generalize Orlov's blow up formula [O04] to possibly singular local complete intersection centres. Second, we introduce refined blowing up of linear category along base--locus, and show that this operation is dual to taking linear section. Finally, as an application we produce examples of Calabi--Yau manifolds which admits Calabi--Yau categories fibrations over projective spaces.
arXiv comment41 pages. Comments are welcome! v2: applications to CY fibrations added
References in corpus (8)
- Triangulated categories of singularities and D-branes in Landau-Ginzburg models
- Semiorthogonal decomposition for algebraic varieties
- Hodge theory and derived categories of cubic fourfolds
- Base change for semiorthogonal decompositions
- Semiorthogonal decompositions in algebraic geometry
- The K3 category of a cubic fourfold
- Categorical Plücker Formula and Homological Projective Duality
- Categorical duality between joins and intersections