Seven combinatorial problems around isolated quasihomogeneous singularities

作     者：Hertling, Claus Zilke, Philip 

作者机构：Univ Mannheim Lehrstuhl Math 6 Seminargebaude A 56 D-68131 Mannheim Germany 

出 版 物：《JOURNAL OF ALGEBRAIC COMBINATORICS》 (代数组合学杂志)

年 卷 期：2019年第50卷第4期

页      面：447-482页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：DFG [He2287/4-1] 

主　　题：Isolated quasihomogeneous singularity Weight system Monodromy Characteristic polynomial Combinatorial problems Orlik blocks 32S40 12Y05 05C22 05C25 

摘      要：This paper proposes seven combinatorial problems around formulas for the characteristic polynomial and the spectral numbers of an isolated quasihomogeneous hypersurface singularity. One of them is a new conjecture on the characteristic polynomial. It is an amendment to an old conjecture of Orlik on the integral monodromy of an isolated quasihomogeneous singularity. The search for a combinatorial proof of the new conjecture led us to the seven purely combinatorial problems.