2022/05/19 by Jiamin Li, Li, Jiamin
Mathematics · #13D45 14M12 13H15 #Advanced Combinatorial Mathematics #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2205.09657
openalex publication_date 2022/05/19 · openalex created_date 2022/05/23 · openalex updated_date 2026/07/28
Let S=ℂ[xij] be a polynomial ring of m× n generic variables (resp. a polynomial ring of (2n+1) × (2n+1) skew-symmetric variables) over ℂ and let I (resp. Pf) be the determinantal ideal of maximal minors (resp. sub-maximal pfaffians) of S. Using the representation theoretic techniques introduced in the work of Raicu et al, we study the asymptotic behavior of the length of the local cohomology module of determinantal and pfaffian thickenings for suitable choices of cohomological degrees. This asymptotic behavior is also defined as a notion of multiplicty. We show that the multiplicity in our setting coincides with the degrees of Grassmannian and Orthogonal Grassmannian.