Secant varieties and birational geometry |
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Authors: | Peter Vermeire |
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Institution: | (1) Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, USA (e-mail: petvermi@math.okstate.edu) , US |
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Abstract: | We show how to use information about the equations defining secant varieties to smooth projective varieties in order to construct
a natural collection of birational transformations. These were first constructed as flips in the case of curves by M. Thaddeus
via Geometric Invariant Theory, and the first flip in the sequence was constructed by the author for varieties of arbitrary
dimension in an earlier paper. We expose the finer structure of a second flip; again for varieties of arbitrary dimension.
We also prove a result on the cubic generation of the secant variety and give some conjectures on the behavior of equations
defining the higher secant varieties.
Received: 29 November 1999; in final form: 4 September 2000 / Published online: 23 July 2001 |
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Keywords: | Mathematics Subject Classification (1991): 14E05 |
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