2002/08/08 by Helena Verrill, Verrill, Helena, David Joyner +1 · 1 citation
Mathematics · #14M25 #14Q15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG #msc:14M25 #msc:14Q15
paper · pdf · doi:10.48550/arxiv.math/0208065
71 pages, 35 figures, index
arxiv created 2002/08/08 · openalex publication_date 2002/08/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
These notes survey some basic results in toric varieties over a field with examples and applications. A computer algebra package (written by the second author) is described which deals with both affine and projective toric varieties in any number of dimensions (written in both the software packages MAGMA and GAP). Among other things, the package implements a desingularization procedure for affine toric varieties, constructs some error-correcting codes associated with toric varieties, and computes the Riemann-Roch space of a divisor on a toric variety.