54 research outputs found
On curves with one place at infinity
Let be a plane curve. We give a procedure based on Abhyankar's
approximate roots to detect if it has a single place at infinity, and if so
construct its associated -sequence, and consequently its value
semigroup. Also for fixed genus (equivalently Frobenius number) we construct
all -sequences generating numerical semigroups with this given genus.
For a -sequence we present a procedure to construct all curves having
this associated sequence.
We also study the embeddings of such curves in the plane. In particular, we
prove that polynomial curves might not have a unique embedding.Comment: 14 pages, 2 figure
Uniquely presented finitely generated commutative monoids
A finitely generated commutative monoid is uniquely presented if it has only
a minimal presentation. We give necessary and sufficient conditions for
finitely generated, combinatorially finite, cancellative, commutative monoids
to be uniquely presented. We use the concept of gluing to construct commutative
monoids with this property. Finally for some relevant families of numerical
semigroups we describe the elements that are uniquely presented.Comment: 13 pages, typos corrected, references update
δ-Sequences and Evaluation Codes de ned by Plane Valuations at Infinity
We introduce the concept of δ-sequence. A δ-sequence ∆ generates a well-ordered semigroup
S in Z2 or R. We show how to construct (and compute parameters) for the dual code of any evaluation code associated with a weight function defined by ∆ from the polynomial ring in two indeterminates to a semigroup S as above. We prove that this is a simple procedure which can be understood by considering a particular class of valuations of function fields of surfaces, called plane valuations at infinity. We also give algorithms to construct an unlimited number of
δ-sequences of the diferent existing types, and so this paper provides the tools to know and use a new large set of codes
Local Volumes.
In the present thesis we study a notion of local volume for Cartier divisors on arbitrary blow–ups of normal complex algebraic varieties of dimension greater than one, with a distinguished point. We apply this to study a volume for normal isolated singularities, generalizing work of Wahl on surfaces. We also compare this volume of isolated singularities to a different generalization due to Boucksom, de Fernex, and Favre.Ph.D.MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91517/1/mfulger_1.pd
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