Extensions of Toric Varieties

Sahin M.

ELECTRONIC JOURNAL OF COMBINATORICS, vol.18, no.1, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 1
  • Publication Date: 2011
  • Journal Name: ELECTRONIC JOURNAL OF COMBINATORICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Hacettepe University Affiliated: No

Abstract

In this paper, we introduce the notion of "extension" of a toric variety and study its fundamental properties. This gives rise to infinitely many toric varieties with a special property, such as being set theoretic complete intersection or arithmetically Cohen-Macaulay (Gorenstein) and having a Cohen-Macaulay tangent cone or a local ring with non-decreasing Hilbert function, from just one single example with the same property, verifying Rossi's conjecture for larger classes and extending some results appeared in literature.