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7 papers · 2 filters
Socle degrees, Resolutions, and Frobenius powers
Andrew R. Kustin, Bernd Ulrich
We first describe a situation in which every graded Betti number in the tail of the resolution of may be read from the socle degrees of . Then we apply the abo…
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…
Compositions of consistent systems of rank one discrete valuation rings
William J. Heinzer, Louis J. Ratliff, David E. Rush
Let V be a rank one discrete valuation ring (DVR) on a field F and let L/F be a finite separable algebraic field extension with [L:F] = m. The integral closure of V in L is a Dedek…
A-graded methods for monomial ideals
Christine Berkesch, Laura Felicia Matusevich
We use \ZZ^d-gradings to study d-dimensional monomial ideals. The Koszul functor is employed to interpret the quasidegrees of local cohomology in terms of the geometry of distracti…
Computing j-multiplicity
Koji Nishida, Bernd Ulrich
The j-multiplicity is an invariant that can be defined for any ideal in a Noetherian local ring . It is equal to the Hilbert-Samuel multiplicity if the ideal is -primary…
Stanley depth of complete intersection monomial ideals and upper-discrete partitions
YiHuang Shen
Let be an -generated complete intersection monomial ideal in . We show that the Stanley depth of is $n-\floor{\frac{m}{2}}$. We also study the upper-di…