We construct a model without precipitous ideals but so that for each τ < א3 there is a normal ideal over א1 with generic ultrapower wellfounded up to the image of τ .

Monomial ideals which are generic with respect to either their generators or irreducible components have minimal free resolutions derived from simplicial complexes. For a generic monomial ideal, the associated primes satisfy a saturated chain condition, and the Cohen-Macaulay property implies shellability for both the Scarf complex and the Stanley-Reisner complex. Reverse lexicographic initial ...

We improve certain degree bounds for Gröbner bases of polynomial ideals in generic position. We work exclusively in deterministically verifiable and achievable generic positions of a combinatorial nature, namely either strongly stable position or quasi stable position. Furthermore, we exhibit new dimension(and depth-)dependent upper bounds for the Castelnuovo-Mumford regularity and the degrees ...

We introduce and analyze an interesting quantity, the path integral ideal, governing the flow of generic discrete theories to the continuum limit and greatly increasing their convergence. The said flow is classified according to the degree of divergence of the potential at spatial infinity. Studying the asymptotic behavior of path integral ideals we isolate the dominant terms in the effective p...

The ideal of a Segre variety P1 × · · · × Pt ↪→ P(n1+1)···(nt+1)−1 is generated by the 2-minors of a generic hypermatrix of indeterminates (see [Ha1] and [Gr]). We extend this result to the case of SegreVeronese varieties. The main tool is the concept of “weak generic hypermatrix” which allows us to treat also the case of projection of Veronese surfaces from a set of general points and of Veron...

It is well-known that the Plücker relations generate the ideal of relations of the maximal minors of a generic m× n matrix. In this paper we discuss the relations of t-minors for t < min(m,n). We will exhibit minimal relations in degrees 2 (non-Plücker in general) and 3, and give some evidence for our conjecture that we have found the generating system of the ideal of relations. The approach is...

This paper is concerned with a relationship between the existence of subvarieties of principally polarized abelian varieties (ppav’s) having minimal cohomology class and the (generic) vanishing of certain sheaf cohomology, based on the Generic Vanishing criterion studied in [PP3]. This is in analogy with the well-known equivalence between a subvariety in projective space being of minimal degree...

We study two partial orders on [x1, . . . , xn], the free abelian monoid on {x1, . . . , xn}. These partial orders, which we call the “strongly stable” and the “stable” partial order, are defined by the property that their filters are precisely the strongly stable and the stable monoid ideals. These ideals arise in the study of generic initial ideals.

We show that given a finitely generated standard graded algebra of dimension d over an infinite field, its graded Noether normalizations obey a certain kind of ‘generic exchange’, allowing one to pass between any two of them in at most d steps. We prove analogous generic exchange theorems for minimal reductions of an ideal, minimal complete reductions of a set of ideals, and minimal complete re...

This paper deals with a new challenge in Adaptive Hypermedia and Web-based systems: finding the perfect adaptation language to express, independently from the domain model, the intelligent, adaptive behaviour of personalized Web courseware. The major requirements for the ideal language are: reuse, flexibility, high level semantics, and ease of use. To draw closer to this ideal language, we comp...