Hilbert Series of Residual Intersections

TL;DR

This paper derives explicit formulas for the Hilbert series of residual intersections of schemes, linking them to conormal modules, with applications to secant varieties of surfaces and three-folds.

Contribution

It provides the first explicit formulas for Hilbert series of residual intersections in terms of conormal modules, extending previous theoretical results.

Findings

Formulas for Hilbert series of residual intersections

Applications to secant varieties of surfaces and three-folds

Enhanced understanding of residual intersection properties

Abstract

We find explicit formulas for the Hilbert series of residual intersections of a scheme in terms of the Hilbert series of its conormal modules. In a previous paper we proved that such formulas should exist. We give applications to the dimension of secant varieties of surfaces and three-folds.