2013/07/28 by Neeraj Kumar, Kumar, Neeraj
Mathematics · #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13D02 #Secondary 13S37 #math.AC #math.AG #msc:13D02 #msc:13S37
paper · pdf · doi:10.48550/arxiv.1307.7381
To appear in Journal of Commutative Algebra
arxiv created 2013/07/31 · arxiv updated 2013/08/01
Let S=K[x1,...,xn] be a polynomial ring over a field K and I a homogeneous ideal in S generated by a regular sequence f1,f2,...,fk of homogeneous forms of degree d. We study a generalization of a result of Conca, Herzog, Trung, and Valla [9] concerning Koszul property of the diagonal subalgebras associated to I. Each such subalgebra has the form K[(Ie)ed+c], where c and e are positive integers. For k=3, we extend [9, Corollary 6.10] by proving that K-algebra K[(Ie)ed+c] is Koszul as soon as c >= d/2. We also extend [9, Corollary 6.10] in another direction by replacing the polynomial ring with a Koszul ring.