Equivalence of Coniveaus

TL;DR

This paper proves that the geometric coniveau and Hodge coniveau, two different notions of coniveau on smooth projective varieties over complex numbers, are actually equivalent.

Contribution

It establishes the equivalence between geometric coniveau and Hodge coniveau on smooth projective varieties, clarifying their relationship.

Findings

Geometric coniveau equals Hodge coniveau.

Provides a unified understanding of coniveau in algebraic geometry.

Bridges the gap between geometric and Hodge-theoretic perspectives.

Abstract

On a smooth projective variety over the complex numbers, there is the coniveau from the coniveau filtration, which is called geometric coniveau. On the same variety, there is another coniveau from the maximal sub-Hodge structure, which is called Hodge coniveau. In this paper we show they are equivalent.