The projective dimension of codimension two algebras presented by quadrics

JOURNAL OF ALGEBRA

卷:393

Article

Huneke, Craig¹  Mantero, Paolo²  McCullough, Jason³  Seceleanu, Alexandra⁴ 

[1] Univ Virginia, Dept Math, Charlottesville, VA 22904 USA

[2] Univ Calif Riverside, Dept Math, Riverside, CA 92521 USA

[3] Rider Univ, Dept Math, Lawrenceville, NJ 08648 USA

[4] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA

关键词: Projective dimension;    Quadratic form;    Determinantal ideal;    Free resolution;   

DOI  :  10.1016/j.jalgebra.2013.06.038

来源: Elsevier

【 摘 要 】

Motivated by a question of Stillman, we find a sharp upper bound for the projective dimension of ideals of height two generated by quadrics. In a polynomial ring with arbitrary large number of variables, we prove that ideals generated by n quadrics define cyclic modules with projective dimension at most 2n - 2. We refine this bound according to the multiplicity of the ideal. We ask whether tight upper bounds for the projective dimension of ideals generated by quadrics can be expressed only in terms of their height and number of minimal generators. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free