Postulation of general quintuple fat point schemes in P^3

TL;DR

This paper investigates the postulation of general multiple fat point schemes in P^3, proving good postulation for degrees d ≥ 11 and classifying exceptions in degrees 9 and 10, using theoretical and computational methods.

Contribution

It provides new results on the postulation of complex fat point schemes in P^3, combining classical lemmas with computer-assisted proofs.

Findings

Good postulation for degrees d ≥ 11 in characteristic 0.

Classification of exceptions in degrees 9 and 10.

Use of Horace differential lemma with computational verification.

Abstract

We study the postulation of a general union Y of double, triple, quartuple and quintuple points of P^3. In characteristic 0, we prove that Y has good postulation in degree $d\ge 11$. The proof is based on the combination of the Horace differential lemma with a computer-assisted proof. We also classify the exceptions in degree 9 and 10.