On $T$-maps and ideals of antiderivatives of hypersurface singularities

Мұқаба

Дәйексөз келтіру

Толық мәтін

Ашық рұқсат Ашық рұқсат
Рұқсат жабық Рұқсат берілді
Рұқсат жабық Тек жазылушылар үшін

Аннотация

Mather–Yau's theorem leads to an extensive study about moduli algebras of isolated hypersurface singularities. In this paper, the Tjurina ideal is generalized as $T$-principal ideals of certain $T$-maps for Noetherian algebras. Moreover, we introduce the ideal of antiderivatives of a $T$-map, which creates many new invariants. Firstly, we compute two new invariants associated with ideals of antiderivatives for ADE singularities and conjecture a general pattern of polynomial growth of these invariants.Secondly, the language of $T$-maps is applied to generalize the well-known theorem that the Milnor number of a semi quasi-homogeneous singularity is equal to that of its principal part. Finally, we use the $T$- fullness and $T$-dependence conditions to determine whether an ideal is a $T$-principal ideal and provide a constructive way of giving a generator of a $T$-principal ideal. As a result, the problem about reconstruction of a hypersurface singularitiy from its generalized moduli algebras is solved. It generalizes the results of Rodrigues in the cases of the $0$th and $1$st moduli algebra, which inspired our solution.Bibliography: 24 titles.

Авторлар туралы

Quan Shi

Department of Mathematical Sciences, School of Sciences, Tsinghua University; Tsinghua University

Хат алмасуға жауапты Автор.
Email: shiq20@mails.tsinghua.edu.cn

Stephen Yau

Beijing Institute of Mathematical Sciences and Applications; Department of Mathematical Sciences, School of Sciences, Tsinghua University

Email: yau@uic.edu

PhD, Professor

Huaiqing Zuo

Department of Mathematical Sciences, School of Sciences, Tsinghua University

Email: hqzuo@mail.tsinghua.edu.cn

Әдебиет тізімі

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