Addition-deletion results for plus-one generated curves

Author:

Anca Măcinic, Piotr Pokora

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Commutative Algebra (math.AC)

journal:

date:

2023-10-29 16:00:00

Abstract

In the recent paper A. Dimca proves that when one adds to or deletes a line from a free curve the resulting curve is either free or plus-one generated. We prove two converse statements for plus-one generated curves and we give an additional insight into the original deletion result, and derive a characterisation of free curves in terms of behaviour to addition/deletion of lines. We describe the possible splitting types of the bundle of logarithmic vector fields associated to a plus-one generated curve.

PDF: Addition-deletion results for plus-one generated curves.pdf