Search results for "projective varieties"

showing 2 items of 2 documents

Triple planes with $p_g=q=0$

2019

We show that general triple planes with p_g=q=0 belong to at most 12 families, that we call surfaces of type I,..., XII, and we prove that the corresponding Tschirnhausen bundle is direct sum of two line bundles in cases I, II, III, whereas is a rank 2 Steiner bundle in the remaining cases. We also provide existence results and explicit constructions for surfaces of type I,..., VII, recovering all classical examples and discovering several new ones. In particular, triple planes of type VII provide counterexamples to a wrong claim made in 1942 by Bronowski.

Discrete mathematicsSteiner bundleApplied MathematicsGeneral Mathematics010102 general mathematicsprojective varietiesspaceadjunction theorysurfaces01 natural sciences14E20bundlesunstable hyperplanesMathematics - Algebraic GeometryTriple plane0103 physical sciencesFOS: Mathematics010307 mathematical physicsarrangements[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]0101 mathematicsMSc: Primary 14E20 14J60Algebraic Geometry (math.AG)Mathematicscovers
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Homological Projective Duality for Determinantal Varieties

2016

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.

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]
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