A question of Nori, Segre classes of ideals and other applications

TL;DR

This paper develops generalized algebraic tools like the moving lemma and addition/subtraction principles, then applies them to study Nori's question on homotopy of projective module sections and to extend results on Segre classes of ideals.

Contribution

It introduces more general versions of key algebraic principles and applies them to longstanding questions in algebraic geometry and ideal theory.

Findings

Proved generalized moving lemma, addition, and subtraction principles.

Extended results on Segre classes of ideals.

Addressed Nori's question on homotopy of projective modules.

Abstract

In this paper, we prove the moving lemma, addition and subtraction principles, in a more general setup than the available ones. We apply these results to explore a question of Nori on homotopy of sections of projective modules. As another application, we investigate the Segre class of ideals, extending the existing results.