๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Applications of Some Properties of the Canonical Module in Computational Projective Algebraic Geometry

โœ Scribed by Marc Chardin

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
308 KB
Volume
29
Category
Article
ISSN
0747-7171

No coin nor oath required. For personal study only.

โœฆ Synopsis

We here develop some new algorithms for computing several invariants attached to a projective scheme (dimension, Hilbert polynomial, unmixed part,... ) that are based on liaison theory and therefore connected to properties of the canonical module. The main features of these algorithms are their simplicity and the fact that their complexity is controlled by the complexity of the output, when it exceeds a linear function on the degrees of the input. We also give bounds for the Castelnuovo-Mumford regularity (which controls the complexity of the output) in low dimension, and give a reasonable algorithm to check smoothness of the unmixed part (one case where good bounds are known for complexity).

๐Ÿ“œ SIMILAR VOLUMES

Algebras, Projective Geometry, Mathemati
Algebras, Projective Geometry, Mathematical Logic, and Constructing the World: Intersections in the Philosophy of Mathematics of A. N. Whitehead
โœ I. Grattan-Guinness ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 218 KB

A. N. Whitehead (1861N. Whitehead ( -1947) ) contributed notably to the foundations of pure and applied mathematics, especially from the late 1890s to the mid 1920s. An algebraist by mathematical tendency, he surveyed several algebras in his book Universal Algebra (1898). Then in the 1900s he joined

Some Simple Projective Brauer Quotients
Some Simple Projective Brauer Quotients of Simple Modules for the Symmetric Groups in Characteristic Two
โœ Luis Valero-Elizondo ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 159 KB

2แŽ22 the number of simple kS -modules equals the number of weights for S , n n where S is the symmetric group on n symbols and k is a field of characteristic n p ) 0. In this paper we answer the question, ''When is the Brauer quotient of a simple F S -module V with respect to a subgroup H of S both

Application of the MuMATH computer algeb
Application of the MuMATH computer algebra system to sets of first order kinetic equations of significance in chemistry
โœ Carl Trindle ๐Ÿ“‚ Article ๐Ÿ“… 1987 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 494 KB

Analytical solutions to systems of first order differential equations have long been available; however, they become so involved that they are seldom used. Numerical simulations are preferred in practice, although they produce bulky output that is difficult to interpret. Even worse, they are occasio