Linear systems on a class of anticanonical rational threefolds

TL;DR

This paper develops an explicit algorithm to compute the dimension of global sections of line bundles on a specific class of rational threefolds obtained by blowing up P^3 along points on an elliptic quartic curve.

Contribution

It introduces a new algorithm for calculating the dimension of H^0(X,L) on a class of anticanonical rational threefolds, expanding computational tools in algebraic geometry.

Findings

Algorithm successfully computes H^0 dimensions for given line bundles.

Provides explicit formulas for line bundle cohomology on these threefolds.

Enhances understanding of linear systems on complex threefolds.

Abstract

Let X be the blow-up of the three dimensional complex projective space along r general points of a smooth elliptic quartic curve B of P^3 and let L be any line bundle of X. The aim of this paper is to provide an explicit algorithm for determining the dimension of H^0(X,L).