2020/08/03 by Karim Adiprasito, Geva Yashfe, Adiprasito, Karim +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2008.01044
openalex publication_date 2020/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide a new foundation for combinatorial commutative algebra and Stanley-Reisner theory using the partition complex introduced in [Adi18]. One of the main advantages is that it is entirely self-contained, using only a minimal knowledge of algebra and topology. On the other hand, we also develop new techniques and results using this approach. In particular, we provide - A novel, self-contained method of establishing Reisner's theorem and Schenzel's formula for Buchsbaum complexes. - A simple new way to establish Poincaré duality for face rings of manifolds, in much greater generality and precision than previous treatments. - A "master-theorem" to generalize several previous results concerning the Lefschetz theorem on subdivisions. - Proof for a conjecture of Kühnel concerning triangulated manifolds with boundary.