We find a minimal generating set for the defining ideal of the schematic intersection of the set of diagonal matrices with the closure of the conjugacy class of a nilpotent matrix indexed by a hook partition. The structure of this ideal allows us to compute its minimal free resolution and give an explicit description of the graded Betti numbers, and study its Hilbert series and regularity.

We present a constraint-based syntax-semantics interface for the construction of RMRS (Robust Minimal Recursion Semantics) representations from shallow grammars. The architecture is designed to allow modular interfaces to existing shallow grammars of various depth – ranging from chunk grammars to context-free stochastic grammars. We define modular semantics construction principles in a typed fe...

Given multigraded free resolutions of two monomial ideals we construct a multigraded free resolution of the sum of the two ideals. Introduction Let K be a field, S = K[x1, . . . , xn] the polynomial ring in n variables over K, and let I and J be two monomial ideals in S. Suppose that F is a multigraded free S-resolution of S/I and G a multigraded free S-resolution of S/J . In this note we const...

Minimal resolution restricts the applicability of resolution and factorization to minimal literals. Minimality is an abstract criterion. It is shown that if the minimality criterion satisfies certain properties, minimal resolution is sound and complete. Hyper-resolution, ordered resolution and lock resolution are known instances of minimal resolution. We also introduce new instances called list...

We consider a local (or standard graded) ring R R with ideals alttext="script upper I prime"> <mml:mrow class="MJX-TeXAtom-O...

We propose a notion of minimal free resolutions for differential modules, and we prove existence uniqueness results such resolutions. also take the first steps toward studying structure modules. Our main result in this direction explains sense which resolution module is deformation its homology; leads to structural that mirror classical theorems about