Standard classes on the blow-up of P^n at points in very general position

TL;DR

This paper investigates the dimensions of linear systems on blow-ups of projective spaces at points in very general position, proposing algorithms and Maple codes based on conjectures to analyze these systems.

Contribution

It introduces new conjectures and computational tools for studying linear systems on blow-ups of projective spaces, advancing understanding in algebraic geometry.

Findings

Algorithms and Maple codes for linear system analysis

Support for conjectures on dimension calculations

Enhanced computational methods in algebraic geometry

Abstract

We study conjectures on the dimension of linear systems on the blow-up of P^2 and P^3 at points in very general position. We provide algorithms and Maple codes based on these conjectures.