Free resolutions for special tangent cones. (English) Zbl 0558.14008

Robbiano, Lorenzo; Valla, Giuseppe

Commutative algebra, Proc. Conf., Trento/Italy 1981, Lect. Notes Pure Appl. Math. 84, 253-274 (1983).

[For the entire collection see Zbl 0493.00004.]
In this paper the authors start with the notion of a standard base of an ideal in a local ring (in definition 1.6, \(f^*_ 1,...,f^*_ r\) should be a minimal set of generators of \(J^*)\) and investigate various properties of a standard base, particularly in relation to the elements (resp. their initial forms) forming a regular sequence, and the Koszul complex corresponding to the initial forms. The paper concludes with some application and examples.

Reviewer: B.Singh

MSC:

14E15	Global theory and resolution of singularities (algebro-geometric aspects)
13E15	Commutative rings and modules of finite generation or presentation; number of generators
14B05	Singularities in algebraic geometry

Keywords:

tangent cone; minimal set of generators; standard base; Koszul complex