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• W1890560012 abstract "Small codimensional embedded manifolds defined by equations of small degree are Fano and covered by lines. They are complete intersections exactly when the variety of lines through a general point is so and has the right codimension. This allows us to prove the Hartshorne Conjecture for manifolds defined by quadratic equations and to obtain the list of such Hartshorne manifolds. Using the geometry of the variety of lines through a general point, we characterize scrolls among dual defective manifolds. This leads to an optimal bound for the dual defect, which improves results due to Ein. We discuss our conjecture that every dual defective manifold with cyclic Picard group should also be secant defective, of a very special type, namely a local quadratic entry locus variety." @default.
• W1890560012 created "2016-06-24" @default.
• W1890560012 creator A5060692499 @default.
• W1890560012 creator A5061833852 @default.
• W1890560012 date "2009-09-15" @default.
• W1890560012 modified "2023-09-27" @default.
• W1890560012 title "Manifolds covered by lines, defective manifolds and a restricted Hartshorne Conjecture" @default.
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• W1890560012 hasPublicationYear "2009" @default.
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