会場

埼玉大学 大学院理工学研究科棟5階 数学研究室1 （ このページ の15番の建物）

Tea and coffee

講演者

Carles Bivia Ausina 氏 (Universitat Politecnica de Valencia)

タイトル

Log-canonical threshold, diagonal ideals and mixed multiplicities

アブストラクト

We characterize the ideals $I$ of finite colength of the ring $\mathcal O_n$ of complex analytic functions germs $(\mathbb C^n,0)\to \mathbb C$ whose integral closure is equal to the integral closure of an ideal generated by pure monomials. The computation of the integral closure of a given ideal is an important problem both in commutative algebra and singularity theory. The mentioned characterization, which is motivated by an inequality proven by Demailly and Pham, is given in terms of the log canonical threshold of $I$ and the sequence of mixed multiplicities of $I$. Motivated by a result of Hickel, we relate this topic with the question of characterizing the ideals of $\mathcal O_n$ whose multiplicity is equal to the product of their mixed \L ojasiewicz exponents and derive some consequences of our study to singularities of function germs.

Seminar dinner