6533b7d3fe1ef96bd1260b2e

RESEARCH PRODUCT

Homological Projective Duality for Determinantal Varieties

Michele BolognesiMarcello BernardaraDaniele Faenzi

subject

Pure mathematicsGeneral MathematicsHomological projective dualitySemi-orthogonal decompositionsDeterminantal varieties01 natural sciencesDerived categoryMathematics - Algebraic GeometryMathematics::Algebraic GeometryMathematics::Category Theory0103 physical sciencesFOS: MathematicsProjective spaceCategory Theory (math.CT)0101 mathematicsAlgebraic Geometry (math.AG)Categorical variableMathematics::Symplectic GeometryPencil (mathematics)Projective varietyComputingMilieux_MISCELLANEOUSMathematicsDiscrete mathematicsDerived category010308 nuclear & particles physicsProjective varietiesComplex projective space010102 general mathematicsFano varietyMathematics - Category TheoryCodimension[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]Rationality questions[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]

description

In this paper we prove Homological Projective Duality for crepant categorical resolutions of several classes of linear determinantal varieties. By this we mean varieties that are cut out by the minors of a given rank of a n x m matrix of linear forms on a given projective space. As applications, we obtain pairs of derived-equivalent Calabi-Yau manifolds, and address a question by A. Bondal asking whether the derived category of any smooth projective variety can be fully faithfully embedded in the derived category of a smooth Fano variety. Moreover we discuss the relation between rationality and categorical representability in codimension two for determinantal varieties.

yearjournalcountryeditionlanguage
2016-06-01
http://arxiv.org/abs/1410.7803