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Abstract
The k-secant degree is studied with a combinatorial approach. A planar toric degeneration of any projective toric surface X corresponds to a regular unimodular triangulation D of the polytope defining X. If the secant ideal of the initial ideal of X with respect to D coincides with the initial ideal of the secant ideal of X, then D is said to be delightful and the k-secant degree of X is easily computed. We establish a lower bound for the 2- and 3-secant degree, by means of the combinatorial geometry of non-delightful triangulations.
Published Online: 2013-03-29
Published in Print: 2013-04
© 2013 by Walter de Gruyter GmbH & Co.
