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摘要翻译：
给出了参数曲面和线性精度概念的精确数学表达式，并建立了它们的基本性质。我们把线性精度与特定线性投影的几何关系起来，给出了一个贴片具有线性精度的必要条件（而且是相当限制性的）。重点讨论了Krasauskas的toric曲面的线性精度，证明了它等价于CP^D上的一个有理映射是双形同构的。最后，在代数统计中建立了曲面曲面的线性预紧度与离散指数族的最大似然度之间的联系，并给出了迭代比例拟合在曲面曲面计算中的应用。
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英文标题：
《Linear precision for parametric patches》
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作者：
Luis Garcia-Puente and Frank Sottile
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最新提交年份：
2009
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
We give a precise mathematical formulation for the notions of a parametric patch and linear precision, and establish their elementary properties. We relate linear precision to the geometry of a particular linear projection, giving necessary (and quite restrictive) conditions for a patch to possess linear precision. A main focus is on linear precision for Krasauskas' toric patches, which we show is equivalent to a certain rational map on CP^d being a birational isomorphism. Lastly, we establish the connection between linear presision for toric surface patches and maximum likelihood degree for discrete exponential families in algebraic statistics, and show how iterative proportional fitting may be used to compute toric patches.
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PDF链接：
https://arxiv.org/pdf/0706.2116
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