2013/03/04 by Jared L. Painter, Painter, Jared, Jared Painter
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras #math.AC
paper · pdf · doi:10.48550/arxiv.1303.0735
17 pages
arxiv created 2013/03/04 · openalex publication_date 2013/03/04 · arxiv updated 2013/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We will explore some properties of minimal graded free resolutions of R/I, where R is a trivariate polynomial ring over a field and I is a monomial ideal. Our focus will be to consider a specific form of the resolutions when I is primary to the homogeneous maximal ideal. We will identify certain characteristics of the last matrix of these resolutions, and observe differences in the resolutions for generic ideals in comparison to non-generic ideals. Finally, we learn how to identify whether I is generic by knowing the structure of the last matrix in the minimal free resolution of R/I.