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Primary Decomposition: Algorithms and Comparisons
TLDR
The Hilbert series and degree bounds play significant roles in computational invariant theory. Expand
Computing in Algebraic Geometry: A Quick Start using SINGULAR
Introductory Remarks on Computer Algebra.- 1 Basic Notations and Ideas: A Historical Account.- 2 Basic Computational Problems and Their Solution.- 3 An Introduction to SINGULAR.- Practical Session IExpand
Syzygies of Abelian and Bielliptic Surfaces in ℙ4
So far only six families of smooth irregular surfaces are known to exist in P^4 (up to pullbacks by suitable finite covers of P^4). These are the elliptic quintic scrolls, the minimal abelian andExpand
Non-general Type Surfaces in P4: Some Remarks on Bounds and Constructions
Sheaf algorithms using the exterior algebra
In this chapter we explain constructive methods for computing the cohomology of a sheaf on a projective variety. We also give a construction for the Beilinson monad, a tool for studying the sheafExpand
The use of bad primes in rational reconstruction
TLDR
A standard method for computing a rational number from its values modulo a collection of primes is to determine its value modulo the product of the primes via Farey sequences for rational reconstruction. Expand
The Normalization: a new Algorithm, Implementation and Comparisons
We present a new algorithm for computing the normalization \(\bar{R}\) of a reduced affine ring R, together with some remarks on efficiency based on our experience with an implementation of thisExpand
Computing integral bases via localization and Hensel lifting
We present a new algorithm for computing integral bases in algebraic function fields, or equivalently for constructing the normalization of a plane curve. Our basic strategy makes use of localizationExpand
An elliptic conic bundle in P^4 arising from a stable rank-3 vector bundle
In this note we show the existence of a family of elliptic conic bundles in P^4 of degree 8. This family has been overlooked and in fact falsely ruled out in a series of classification papers. OurExpand
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