Gröbner basis and free resolution of the ideal of 2-minors of a 2 × n matrix of linear forms^*

^*AMS Mathematics Subject Classifcation (1991): 13D03, 13D02, 13P10.

Abstract

We give a Gröbner basis for the ideal of 2-minors of a 2 × n utiatrix of linear forms. The minimal free resolution of such an ideal is obtained in [4] when the corresponding Kronecker-Weierstrass normal form has no iiilpotent blocks. For the general case, using this result, the Grobner basis and the Eliahou-Kervaire resolution for stable monomial ideals, we obtain a free resolution with the expected regularity. For a specialization of the defining ideal of ordinary pinch points, as a special case of these ideals, we provide a minimal free resolution explicitly in terms of certain Koszul complex.

^*AMS Mathematics Subject Classifcation (1991): 13D03, 13D02, 13P10.

^†Partially supported by Institutefor Studies in Theoretical Phusics and Mathematics (IPM).

^*AMS Mathematics Subject Classifcation (1991): 13D03, 13D02, 13P10.

^†Partially supported by Institutefor Studies in Theoretical Phusics and Mathematics (IPM).

Notes

^*AMS Mathematics Subject Classifcation (1991): 13D03, 13D02, 13P10.

^†Partially supported by Institutefor Studies in Theoretical Phusics and Mathematics (IPM).