Secant varieties and birational geometry

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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.

Original languageEnglish
Pages (from-to)75-95
Number of pages21
JournalMathematische Zeitschrift
Volume242
Issue number1
DOIs
StatePublished - 2002

Fingerprint

Dive into the research topics of 'Secant varieties and birational geometry'. Together they form a unique fingerprint.

Cite this