2001/01/29 by Mina Teicher, M. Teicher, Teicher, M. +2
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Rings, Modules, and Algebras #math.AG
paper · pdf · doi:10.48550/arxiv.math/0101233
arxiv created 2001/01/29 · openalex publication_date 2001/01/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we prove certain Hurwitz equivalence properties of Bn. In particular we prove that for n=3 every two Artin's factorizations of Δ3 2 of the form Hi1 ... Hi6, Fj1 ... Fj6 (with ik, jk ∈ \1,2 \) where \H1, H2 \, \F1, F2 \ are frames, are Hurwitz equivalent. The proof provided here is geometric, based on a newly defined frame type. The results will be applied to the classification of algebraic surfaces up to deformation. It is already known that there exist surfaces that are diffeomorphic to each other but are not deformations of each other (Manetti example). We are constructing a new invariant based on Hurwitz equivalence class of factorization, to distinguish among diffeomorphic surfaces which are not deformation of each other.