ON THE SEGRE UPPER BOUND OF THE REGULARITY FOR NON-FAT POINT SCHEMES IN PROJECTIVE SPACES

E Ballico

doi:10.12732/ijpam.v102i2.9

Abstract

We study the generalized Segre bound in projective space (mainly in the plane) with respect to zero-dimensional schemes which are more general that the fat point schemes.

Highlights

Z is almost-equimultiple, i.e. |mp − mq| ≤ 1 for all p, q ∈ S ([9])
In this note we look at a similar conjecture for zero-dimensional schemes whose connected components are more general than fat points mpp
We say that Z satisfies the Gconditions in degree d or that (Z, d) satisfies the G-conditions if Z satisfies ⋄ and it satisfies the G-condition in degree d with respect to all positive dimensional linear subspaces of Pn

Summary

Introduction

In this note we look at a similar conjecture for zero-dimensional schemes whose connected components are more general than fat points mpp. Assume n = 2, Z tame and that the G-conditions are satisfied in degree d. It is sufficient to take Z = v ∪ e with v a connected degree 2 scheme, say with support p, and with e either ∅ or a point.

Results

Conclusion