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21 papers · 1 filter
Counting Real Connected Components of Trinomial Curve Intersections and m-nomial Hypersurfaces
Tien-Yien Li, J. Maurice Rojas, Xiaoshen Wang
We prove that any pair of bivariate trinomials has at most 5 isolated roots in the positive quadrant. The best previous upper bounds independent of the polynomial degrees were much…
Affine semiprime algebras of GK dimension one are (still) pi
Christopher J. Pappacena, Lance W. Small, Jeanne Wald
In this note, we give a new proof of the fact that an affine semiprime algebra R of Gelfand-Kirillov dimension 1 satisfies a polynomial identity. Our proof uses only the growth pro…
Sally modules and associated graded rings
Alberto Corso, Claudia Polini, Maria Vaz Pinto
We study the depth properties of the associated graded ring of an m-primary ideal I in terms of numerical data attached to the ideal I. We also find bounds on the Hilbert coefficie…
Families of Simply Connected 4-Manifolds with the Same Seiberg-Witten Invariants
Ronald Fintushel, Ronald J. Stern
This article presents the constructions of new infinite families of smooth 4-manifolds with the property that any two manifolds in the same family are homeomorphic and, from their…
A generalized Dedekind-Mertens lemma and its converse
Alberto Corso, William Heinzer, Craig Huneke
We study content ideals of polynomials and their behavior under multiplication. We give a generalization of the Lemma of Dedekind-Mertens and prove the converse under suitable dime…
Core and residual intersections of ideals
Alberto Corso, Claudia Polini, Bernd Ulrich
D. Rees and J. Sally defined the core of an -ideal as the intersection of all minimal reductions of . However, it is not easy to give an explicit characterization o…