Quadratic complete intersections

JOURNAL OF ALGEBRA

卷:571

Article

Eisenbud, David¹  Peeva, Irena²  Schreyer, Frank-Olaf³ 

[1] Univ Calif Berkeley, Math Dept, Berkeley, CA 94720 USA

[2] Cornell Univ, Math Dept, Ithaca, NY 14853 USA

[3] Univ Saarland, Math Dept, Campus E2 4, D-66123 Saarbrucken, Germany

关键词: Syzygies;    Complete intersections;    Matrix factorizations;    Quadrics;    Clifford algebras;    Enveloping algebras;   

DOI  :  10.1016/j.jalgebra.2019.11.031

来源: Elsevier

【 摘 要 】

We study Betti numbers of graded finitely generated modules over a quadratic complete intersection. In the case of codimension 1, we give a natural class of quadratic forms Q whose Clifford algebras are division rings, and deduce the possible Betti numbers of modules over the hypersurfaces Q = 0. Our approach leads to a new version of the Betti degree Conjecture. In higher codimensions, we obtain formulas for the Betti numbers in terms of the ranks of certain free modules in a higher matrix factorization. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free