Flash Geometry of Algebraic Curves
Algebraic Geometry
2010-09-17 v1
Abstract
In this paper, we develop the theory of flashes of an algebraic curve. We show that the theory is birationally invariant in a sense which we will make more precise below. We also show how the theory provides a foundation for the method of asymptotic degenerations, a particular class of degenerations of plane projective algebraic curves. In particular, we consider the geometrical technique in relation to the Severi problem of degenerating nodal curves to lines in general position, and correct Severi's original proof of his conjecture.
Keywords
Cite
@article{arxiv.1009.3219,
title = {Flash Geometry of Algebraic Curves},
author = {Tristram de Piro},
journal= {arXiv preprint arXiv:1009.3219},
year = {2010}
}