scholarly journals Degeneration of linear systems through fat points on $K3$ surfaces

2004 ◽  
Vol 357 (9) ◽  
pp. 3673-3682 ◽  
Author(s):  
Cindy De Volder ◽  
Antonio Laface
Keyword(s):  
Linear Systems ◽  
K3 Surfaces ◽  
Fat Points

scholarly journals Linear systems on generic $K3$ surfaces

2005 ◽  
Vol 12 (4) ◽  
pp. 481-489
Author(s):  
Cindy De Volder ◽  
Antonio Laface
Keyword(s):  
Linear Systems ◽  
K3 Surfaces

scholarly journals Homaloidal nets and ideals of fat points II: Subhomaloidal nets

2017 ◽  
Vol 27 (06) ◽  
pp. 677-715 ◽  
Author(s):  
Zaqueu Ramos ◽  
Aron Simis
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Good Deal ◽  
Detailed Examination ◽  
Symbolic Power ◽  
Fat Points ◽  
Higher Dimensional ◽  
General Plane ◽  
Classical Arithmetic ◽  
The Ideal

This work is a natural sequel to a previous paper by the authors in that it tackles problems of the same nature. Here, one aims at the ideal theoretic and homological properties of an ideal of general plane fat points for which the corresponding second symbolic power has virtual multiplicities of a proper homaloidal type. For this purpose, one carries a detailed examination of the underlying linear system at the initial degree, where a good deal of the results depends on the method of 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 [Formula: see text] 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.

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