Abstract
Let be a convex polygon with vertices. The associated Wachspress surface is a fundamental object in approximation theory, defined as the image of the rational map
determined by the Wachspress barycentric coordinates for . We show is a regular map on a blowup of and, if , is given by a very ample divisor on so has a smooth image . We determine generators for the ideal of and prove that, in graded lex order, the initial ideal of is given by a Stanley–Reisner ideal. As a consequence, we show that the associated surface is arithmetically Cohen–Macaulay and of Castelnuovo–Mumford regularity and determine all the graded Betti numbers of .
Citation
Corey Irving. Hal Schenck. "Geometry of Wachspress surfaces." Algebra Number Theory 8 (2) 369 - 396, 2014. https://doi.org/10.2140/ant.2014.8.369
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