Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Secant Varieties and Birational Geometry   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.

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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th