Triple-Point Defective Ruled Surfaces

TL;DR

This paper classifies triple-point defective very ample linear systems on ruled surfaces, extending previous work by removing the regularity assumption and providing a comprehensive classification.

Contribution

It removes the regularity assumption and fully classifies triple-point defective very ample linear systems on ruled surfaces.

Findings

Triple-point defective systems only exist on ruled surfaces.

Classification of such systems on ruled surfaces.

Extension of previous results without regularity assumption.

Abstract

In arXive:0705.3912 we studied triple-point defective very ample linear systems on regular surfaces, and we showed that they can only exist if the surface is ruled. In the present paper we show that we can drop the regularity assumption, and we classify the triple-point defective very ample linear systems on ruled surfaces.