Matrix representations for toric parametrizations

Details Matrix representations for toric parametrizations Matrix representations for toric parametrizations

2008-07-30

arxiv.org/abs/0807.4802v1

Mathematics

Algebraic Geometry

20 pages

Scientific paper

In this paper we show that a surface in P^3 parametrized over a 2-dimensional toric variety T can be represented by a matrix of linear syzygies if the base points are finite in number and form locally a complete intersection. This constitutes a direct generalization of the corresponding result over P^2 established in [BJ03] and [BC05]. Exploiting the sparse structure of the parametrization, we obtain significantly smaller matrices than in the homogeneous case and the method becomes applicable to parametrizations for which it previously failed. We also treat the important case T = P^1 x P^1 in detail and give numerous examples.

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