Mathematical Research Letters

Volume 21 (2014)

Number 5

On dual defective manifolds

Pages: 1137 – 1154

DOI: https://dx.doi.org/10.4310/MRL.2014.v21.n5.a10

Authors

Paltin Ionescu (Dipartimento di Matematica, Università Degli Studi di Ferrara, Italy; and Institute of Mathematics of the Romanian Academy, Bucharest, Romania)

Francesco Russo (Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Italy)

Abstract

An embedded manifold is dual defective if its dual variety is not a hypersurface. 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 also discuss our conjecture that every dual defective manifold with cyclic Picard group should be secant defective, of a very special type, namely a local quadratic entry locus variety.

Keywords

Fano manifold, covered by lines, dual and secant defective, scroll

2010 Mathematics Subject Classification

14J45, 14Mxx, 14Nxx

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Published 9 December 2014