# Whitney, Kuo-Verdier and Lipschitz stratifications for the surfaces y^a = t^b x^c +x^d

## TL;DR

This paper characterizes various canonical stratifications, including Whitney, Kuo-Verdier, and Mostowski regularities, for a family of algebraic surfaces defined by specific polynomial equations, in both real and complex contexts.

## Contribution

It explicitly describes the stratifications satisfying multiple regularity conditions for a family of algebraic surfaces, extending understanding in both real and complex cases.

## Key findings

- Explicit stratifications for the surfaces y^a = t^b x^c + x^d.
- Comparison of Whitney, Kuo-Verdier, and Mostowski regularities.
- Applicability to both real and complex algebraic surfaces.

## Abstract

We specify the canonical stratifications satisfying respectively Whitney (a)-regularity, Whitney (b)-regularity, Kuo-Verdier (w)-regularity, and Mostowski (L)-regularity for the family of surfaces y^a = t^b x^c + x^d, where a, b, c, d are positive integers, in both the real and complex cases.