Homological projective duality for determinantal varieties
Copyright policy )Homological projective duality for determinantal varieties
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.
23 pages. To appear on Advances in Math
[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], Derived categories and commutative rings, Sheaves, derived categories of sheaves, etc., homological projective duality, Mathematics - Category Theory, derived category, projective varieties, Determinantal varieties, Syzygies, resolutions, complexes and commutative rings, 510, Mathematics - Algebraic Geometry, rationality questions, FOS: Mathematics, determinantal varieties, Category Theory (math.CT), [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], semi-orthogonal decompositions, Algebraic Geometry (math.AG)
[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], Derived categories and commutative rings, Sheaves, derived categories of sheaves, etc., homological projective duality, Mathematics - Category Theory, derived category, projective varieties, Determinantal varieties, Syzygies, resolutions, complexes and commutative rings, 510, Mathematics - Algebraic Geometry, rationality questions, FOS: Mathematics, determinantal varieties, Category Theory (math.CT), [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], semi-orthogonal decompositions, Algebraic Geometry (math.AG)
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