The maximum likelihood degree of a very affine variety
The maximum likelihood degree of a very affine variety
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DOI：
10.1112/s0010437x13007057
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发表时间：
2013-08-01
影响因子：
1.8
通讯作者：
Huh, June
中科院分区：
文献类型：
--
作者：
Huh, June
我们证明了一个光滑的非常仿射簇的极大似然度等于符号拓扑欧拉特征。这推广了Orlik和Terao对Varchenko关于超平面安排的补充的猜想的解决方案，以平滑非常仿射的品种。对于在无穷远处满足一般性条件的非常仿射的品种，结果进一步加强到与Chern-Schwartz-MacPherson类的临界点的品种。加强版恢复了Denham等人关于排列补的几何删除限制公式，推广了Kouchnirenko关于非退化超曲面的牛顿多面体定理.
We show that the maximum likelihood degree of a smooth very affine variety is equal to the signed topological Euler characteristic. This generalizes Orlik and Terao's solution to Varchenko's conjecture on complements of hyperplane arrangements to smooth very affine varieties. For very affine varieties satisfying a genericity condition at infinity, the result is further strengthened to relate the variety of critical points to the Chern-Schwartz-MacPherson class. The strengthened version recovers the geometric deletion restriction formula of Denham et al. for arrangement complements, and generalizes Kouchnirenko's theorem on the Newton polytope for nondegenerate hypersurfaces.