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14 papers · 1 filter
Divisors on Rational Normal Scrolls
Andrew R. Kustin, Claudia Polini, Bernd Ulrich
Let be the homogeneous coordinate ring of a rational normal scroll. The ring is equal to the quotient of a polynomial ring by the ideal generated by the two by two mino…
A characterization of Gorenstein Hilbert functions in codimension four with small initial degree
Juan C. Migliore, Uwe Nagel, Fabrizio Zanello
The main goal of this paper is to characterize the Hilbert functions of all (artinian) codimension 4 Gorenstein algebras that have at least two independent relations of degree four…
Normalization of Ideals and Briancon-Skoda Numbers
Claudia Polini, Bernd Ulrich, Wolmer V. Vasconcelos
We establish bounds for the coefficient of the Hilbert function of the integral closure filtration of equimultiple ideals. These values are shown to help control all…
On the componentwise linearity and the minimal free resolution of a tetrahedral curve
Christopher A. Francisco, Juan C. Migliore, Uwe Nagel
A tetrahedral curve is an unmixed, usually non-reduced, one-dimensional subscheme of projective 3-space whose homogeneous ideal is the intersection of powers of the ideals of the s…
The Multiplicity Conjecture in low codimensions
Juan C. Migliore, Uwe Nagel, Tim Römer
We establish the multiplicity conjecture of Herzog, Huneke, and Srinivasan about the multiplicity of graded Cohen-Macaulay algebras over a field, for codimension two algebras and f…
A formula for the core of an ideal
Claudia Polini, Bernd Ulrich
The core of an ideal is the intersection of all its reductions. For large classes of ideals I we explicitly describe the core as a colon ideal of a power of a single reduction and…