Discriminants of toric varieties. Issue 12 (2nd December 2021)

• Record Type: Journal Article
• Authors: Muñoz, Roberto; Nolla, Álvaro
• Is Part Of: Communications in algebra. Volume 49:Issue 12(2021)
• Page Start: 5109
• Page End: 5128
• Publication Date: 2021-12-02
• Subjects: Discriminants -- first jet bundle -- toric varieties; Primary: 14M25 -- 14N05; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2021.1937639
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: We study the subvariety of singular sections, the discriminant, of a base point free linear system | L | on a smooth toric variety X . On one hand we describe pairs ( X, L ) for which the discriminant is of low dimension. Precisely, we collect some bounds on this dimension and classify those pairs whose dimension differs the bound less than or equal to two. On the other hand we study the degree of the discriminant for some relevant families on polarized toric varieties, describing their minimal values and the region of the ample cone where this minimal is attained.