On the Moduli Space of Quasi-Homogeneous Functions

Author(s)

Camara, Leonardo Meireles ; Soares Ruas, Maria Aparecida

• Document type: Journal article
• Source: BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. N/A, p. 14-pg., 2022-03-20.

Abstract

We relate the moduli space of analytic equivalent germs of reduced quasi-homogeneous functions at (C-2, 0) with their bi-Lipschitz equivalence classes. We show that any non-degenerate continuous family of (reduced) quasi-homogeneous (but not homogeneous) functions with constant Henry-Parushiski invariant is analytically trivial. Further, we show that there are only a finite number of distinct bi-Lipschitz classes among quasi-homogeneous functions with the same Henry-Parushiski invariant providing a maximum quota for this number. Finally, we conclude that the moduli space of bi-Lipschitz equivalent quasi-homogeneous function-germs admits an analytic structure. (AU)

• FAPESP's process: 19/21181-0 - New frontiers in Singularity Theory
• Grantee: Regilene Delazari dos Santos Oliveira
• Support Opportunities: Research Projects - Thematic Grants