Tjurina Number Jumps and Unimodal Hypersurface Singularities in Positive Characteristic

2025/10/02 by H. Ma, Ma, Hongrui, Ying, Aoyu +2
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2510.02619

Abstract

This paper generalizes existing methods to derive stronger bounds on the modality of hypersurface singularities. Our results demonstrate that each sudden jump in the extended Tjurina number necessarily increases the modality. Furthermore, we provide a full classification of unimodal isolated hypersurface singularities in characteristic p > 3 under contact equivalence.

Citations

• Classification of unimodal isolated complete intersection singularities in positive characteristic
• Classification of simple 0-dimensional isolated complete intersection singularities
• On finite determinacy for matrices of power series
• Right unimodal and bimodal singularities in positive characteristic
• Mather-Yau Theorem in Positive Characteristic
• Normal Forms of Hypersurface Singularities in Positive Characteristic

Related

• The Tjurina number for Sebastiani-Thom type isolated hypersurface singularities
• On the quotient of Milnor and Tjurina numbers for two-dimensional isolated hypersurface singularities
• Normal Forms of Hypersurface Singularities in Positive Characteristic
• Hypersurface singularities in positive characteristic
• Right unimodal and bimodal singularities in positive characteristic