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- W4299969679 abstract "Let P_d be a convex polygon with d vertices. The associated Wachspress surface W_d is a fundamental object in approximation theory, defined as the image of the rational map w_d from P^2 to P^{d-1}, determined by the Wachspress barycentric coordinates for P_d. We show w_d is a regular map on a blowup X_d of P^2, and if d>4 is given by a very ample divisor on X_d, so has a smooth image W_d. We determine generators for the ideal of W_d, and prove that in graded lex order, the initial ideal of I(W_d) is given by a Stanley-Reisner ideal. As a consequence, we show that the associated surface is arithmetically Cohen-Macaulay, of Castelnuovo-Mumford regularity two, and determine all the graded betti numbers of I(W_d)." @default.
- W4299969679 created "2022-10-03" @default.
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- W4299969679 date "2013-06-06" @default.
- W4299969679 modified "2023-10-17" @default.
- W4299969679 title "Geometry of Wachspress surfaces" @default.
- W4299969679 doi "https://doi.org/10.48550/arxiv.1306.1445" @default.
- W4299969679 hasPublicationYear "2013" @default.
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