175 citations
- Purdue University West LafayetteUS5 papers
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- University of KentuckyUS3 papers
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- Lomonosov Moscow State UniversityRU2 papers
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- National Radio Astronomy ObservatoryUS2 papers
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- Sapienza University of RomeIT2 papers
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- University of BristolGB2 papers
17 papers · 1 filter
Growth of rank 1 valuation semigroups
Steven Dale Cutkosky, Kia Dalili, Olga Kashcheyeva
We consider the question of which semigroups can occur as the semigroup of positive values of a rank 1 valuation dominating a Noetherian local ring . We give a number o…
Asymptotic vanishing conditions which force regularity in local rings of prime characteristic
Ian Aberbach, Jinjia Li
Let $(R,\m,k)$ be a local (Noetherian) ring of positive prime characteristic and dimension . Let $G_\dt$ be a minimal resolution of the residue field , and for each $i\ge…
Algebraic series and valuation rings over nonclosed fields
Steven Dale Cutkosky, Olga Kashcheyeva
Suppose that is an arbitrary field. Consider the field , which is the quotient field of the ring of formal power series in the variables $x…
New approaches to bounding the multiplicity of an ideal
Christopher A. Francisco
We use the theory of resolutions for a given Hilbert function to investigate the multiplicity conjectures of Huneke and Srinivasan and Herzog and Srinivasan. To prove the conjectur…
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…
Resolutions of small sets of fat points
Christopher Francisco
We investigate the minimal graded free resolutions of ideals of at most n+1 fat points in general position in P^n. Our main theorem is that these ideals are componentwise linear. T…