2017/04/02 by Zaqueu Ramos, Aron Simis, Ramos, Zaqueu +1
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1704.00382
openalex publication_date 2017/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is a natural sequel to [22] in that it tackles problems of the same nature. Here one aims at the ideal theoretic and homological properties of a class of ideals of general plane fat points whose second symbolic powers hold virtual multiplicities of proper homaloidal types. For this purpose one carries a detailed examination of their linear systems at the initial degree, a good deal of the results depending on the method of applying the classical arithmetic quadratic transformations of Hudson--Nagata. A subsidiary guide to understand these ideals through their initial linear systems has been supplied by questions of birationality with source ℙ2 and target higher dimensional spaces. This leads, in particular, to the retrieval of birational maps studied by Geramita--Gimigliano--Pitteloud, including a few of the celebrated Bordiga--White parameterizations.