Cohen-Macaulay Du Bois singularities with a torus action of complexity\n one

2018/06/21 by Antonio Laface, Laface, Antonio, Alvaro Liendo +3
Mathematics · #14B05 (Primary) 14L30 #14M25 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1806.08311

openalex publication_date 2018/06/21 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

Using Altmann-Hausen-Suss description of mathbbT-varieties via\ndivisorial fans and K 'ovacs-Schwede-Smith characterization of Du Bois\nsingularities, we study Cohen-Macaulay Du Bois mathbbT-singularities of\ncomplexity one. We exhibit cohomological criteria for a mathbbT-variety to\nbe Cohen-Macaulay and Du Bois in terms of polyhedral divisors. We give an\nexample of a Cohen-Macaulay Du Bois singularity of complexity one which does\nnot have rational singularities.\n

Related

• The intuitive definition of Du Bois singularities
• On k-Du Bois and k-rational singularities
• Du Bois singularities deform
• On the topology of rational T-varieties of complexity one
• Polyhedral divisors and torus actions of complexity one over arbitrary fields