Inner geometry of complex surfaces: a valuative approach

被引:4
作者
da Silva, Andre Belotto [1 ]
Fantini, Lorenzo [2 ]
Pichon, Anne [1 ]
机构
[1] Aix Marseille Univ, Inst Math Marseille, CNRS, Marseille, France
[2] Ecole Polytech, CNRS, Ctr Math Laurent Schwartz, Palaiseau, France
关键词
SINGULARITIES; L2-COHOMOLOGY; RESOLUTION; SPACES;
D O I
10.2140/gt.2022.26.163
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Given a complex analytic germ (X, 0) in (C-n, 0), the standard Hermitian metric of C-n induces a natural arc-length metric on (X, 0), called the inner metric. We study the inner metric structure of the germ of an isolated complex surface singularity (X, 0) by means of an infinite family of numerical analytic invariants, called inner rates. Our main result is a formula for the Laplacian of the inner rate function on a space of valuations, the nonarchimedean link of (X, 0). We deduce in particular that the global data consisting of the topology of (X, 0), together with the configuration of a generic hyperplane section and of the polar curve of a generic plane projection of (X, 0), completely determine all the inner rates on (X, 0), and hence the local metric structure of the germ. Several other applications of our formula are discussed.
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页码:163 / 219
页数:57
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