0-Borel Fixed Ideals

ON SPECIAL p-BOREL FIXED IDEALS

We define the reduced horseshoe resolution and the notion of conjoined pairs of ideals in order to study the minimal graded free resolution of a class of p-Borel ideals and recover Pardue’s regularity formula for them. It will follow from our technique that the graded betti numbers of these ideals do not depend on the characteristic of the base field k.

Borel-fixed Ideals and Reduction Number

Borel Fixed Initial Ideals of Prime Ideals in Dimension Two

We prove that if the initial ideal of a prime ideal is Borel-fixed and the dimension of the quotient ring is less than or equal to two, then given any non-minimal associated prime ideal of the initial ideal it contains another associated prime ideal of dimension one larger. Let R = k[x1, x2, . . . , xr] be a polynomial ring over a field. We will say that an ideal I ⊆ R has the saturated chain p...

On Borel Fixed Ideals Generated in One Degree

We construct a (shellable) polyhedral cell complex that supports a minimal free resolution of a Borel fixed ideal, which is minimally generated (in the Borel sense) by just one monomial in S = k[x1, x2, ..., xn]; this includes the case of powers of the homogeneous maximal ideal (x1, x2, ..., xn) as a special case. In our most general result we prove that for any Borel fixed ideal I generated in...

Products of Borel fixed ideals of maximal minors

Article history: Received 21 March 2017 Received in revised form 3 April 2017 Accepted 19 May 2017 Available online xxxx MSC: 13D15 13F50 14M12