Effective and Big Divisors on a Projective Symmetric Variety

2009/06/29 by Alessandro Ruzzi, Ruzzi, Alessandro
Arts and Humanities · Health Professions · Mathematics · #(14M17) #14C20 #14L30 #Advanced Algebra and Geometry #Aging, Elder Care, and Social Issues #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Health, Medicine and Society #Hermeneutics and Narrative Identity #Meromorphic and Entire Functions #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0906.5226

openalex publication_date 2009/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe the effective and the big cones of a projective symmetric variety. Moreover, we give a necessary and sufficient combinatorial criterion for the bigness of a nef divisor on a projective symmetric variety. When the variety is toroidal and the divisor is G-stable, such criterion has an explicit geometric interpretation. Finally, we describe the spherical closure of a symmetric subgroup.

Related

• A question on effective strictly nef divisors (with an appendix by Andreas Höring)
• On essentially large divisors
• The Minkowski Equality of Big Divisors
• Pseudo-effective and nef cones on spherical varieties
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