A Batyrev type classification of $Q$--factorial projective toric varieties

Abstract

The present paper is devoted to generalizing, inside the class of projective toric varieties, the classification [Batyrev91], performed by Batyrev in 1991 for smooth complete toric varieties, to the singular $Q$--factorial case. Moreover, in the first part of the paper the Kleinschmidt classification of smooth complete toric varieties of Picard number 2 [Kleinschmidt] is revised.

57 pp, 5 figures. Minor changes: some typos fixed. Major changes: following referee's advise, an example has been subdivided in several examples claryfing concepts introduced in section 1; moreover section 3 has been made more self-contained by introducing several results from our previous papers. Final version to appear in Advances in Geometry

References in corpus (1)

• Z-linear Gale duality and poly weighted spaces (PWS)

Cited by in corpus (2)

• Embedding non-projective Mori Dream Spaces
• Fibration and classification of smooth projective toric varieties of low Picard number