Linear systems on a class of anticanonical rational threefolds
Cindy De Volder, Antonio Laface

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).
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