2017/06/19 by Yairon Cid‐Ruiz, Cid-Ruiz, Yairon · 1 citation
Mathematics · #13A30 #13N10 (Primary) 13D02 #14H50 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1706.06215
openalex publication_date 2017/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let I ⊂ R = \mathbbF[x1,x2] be a height two ideal minimally generated by three homogeneous polynomials of the same degree d, where \mathbbF is a field of characteristic zero. We use the theory of D-modules to deduce information about the defining equations of the Rees algebra of I. Let K be the kernel of the canonical map α: Sym(I) → Rees(I) from the symmetric algebra of I onto the Rees algebra of I. We prove that K can be described as the solution set of a system of differential equations, that the whole bigraded structure of K is characterized by the integral roots of certain b-functions, and that certain de Rham cohomology groups can give partial information about K.