Algebraic Stratified General Position and Transversality

TL;DR

This paper introduces a novel algebraic approach using Whitney interpolation to establish stratified general position and transversality theorems for semialgebraic subsets of algebraic varieties.

Contribution

It develops a new method leveraging Whitney interpolation to achieve stratified transversality in algebraic and semialgebraic contexts.

Findings

Constructs stratified submersive families for algebraic varieties

Establishes stratified general position theorems

Provides tools for transversality in semialgebraic geometry

Abstract

The method of Whitney interpolation is used to construct, for any real or complex projective algebraic variety, a stratified submersive family of self-maps that yields stratified general position and transversality theorems for semialgebraic subsets..