2007/02/22 by Marcel Moralès, Morales, Marcel · 1 citation
Computer Science · Mathematics · #05A15 #13D05.13D45 #13F55 #14B15 #14M05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.math/0702668
openalex publication_date 2007/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the first part of this paper we study scrollers and linearly joined varieties. A particular class of varieties, of important interest in classical Geometry are Cohen--Macaulay varieties of minimal degree. They appear naturally studying the fiber cone of of a codimension two toric ideals. Let I⊂ S be an ideal defining a linearly joined arrangement of varieties: - We compute the depth, and the cohomological dimension. is the connectedness dimension. - We characterize sets of generators of I, and give an effective algorithm to find equations, as an application we compute arithmetical rank. in the case if I defines a union of linear spaces, (ara =projective dimension), in particular this applies to any square free monomial ideal having a 2- linear resolution. - In the case where V is a union of linear spaces, the ideal I, can be characterized by a tableau, which is an extension of a Ferrer (or Young) tableau. - We introduce a new class of ideals called simplicial ideals, ideals defining linearly-joined varieties are a particular case of simplicial ideals.