Lê numbers and Newton diagram

2018/12/03 by Eyral, Christophe, Oleksik, Grzegorz, Różycki, Adam · 1 citation
#14J17 #14J70 #32S25 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.00614

Abstract

We give an algorithm to compute the Lê numbers of (the germ of) a Newton non-degenerate complex analytic function f\colon(ℂⁿ,0) → (ℂ,0) in terms of certain invariants attached to the Newton diagram of the function f+z₁^α₁+⋯ +z_d^α_d, where d is the dimension of the critical locus of f and α₁,…, α_d are sufficiently large integers. This is a version for non-isolated singularities of a famous theorem of A. G. Kouchnirenko. As a corollary, we obtain that Newton non-degenerate functions with the same Newton diagram have the same Lê numbers.

Cited by

• Bekka's (c)-regularity condition and families of line singularities with constant Lê numbers

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