1996/02/28 by Chikashi Miyazaki, Miyazaki, Chikashi, Wolfgang Vogel +1
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #alg-geom #math.AG
paper · pdf · doi:10.48550/arxiv.alg-geom/9602022
LaTeX, 14 pages
arxiv created 1996/02/28 · openalex publication_date 1996/02/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to start a systematic investigation of the arithmetic degree of projective schemes as introduced by D. Bayer and D. Mumford. One main theme concerns itself with the behaviour of this arithmetic degree under hypersurface sections. The notion of arithmetic degree involves the new concept of length-multiplicity of embedded primary ideals. Therefore it is much harder to control the arithmetic degree under a hypersurface section than in the case for the classical degree theory. Nevertheless it has important and interesting applications. We describe such applications to the Castelnuovo-Mumford regularity and to Bezout-type theorems.