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Some Results on Secant Varieties Leading to a Geometric Flip Construction

Published online by Cambridge University Press:  04 December 2007

Peter Vermeire
Peter Vermeire
Affiliation:
Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, U.S.A. E-mail: petvermi@math.okstate.edu
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Abstract

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We study the relationship between the equations defining a projective variety and properties of its secant varieties. In particular, we use information about the syzygies among the defining equations to derive smoothness and normality statements about SecX and also to obtain information about linear systems on the blow up of projective space along a variety X. We use these results to geometrically construct, for varieties of arbitrary dimension, a flip first described in the case of curves by M. Thaddeus via Geometric Invariant Theory.

Keywords

syzygiesflipsvanishing theoremssecant varieties
Type
Research Article
Information
Compositio Mathematica , Volume 125 , Issue 3 , February 2001 , pp. 263 - 282
Copyright
© 2001 Kluwer Academic Publishers