# Injective linear series of algebraic curves on quadrics

## TL;DR

This paper investigates injective linear series on algebraic curves, focusing on cuspidal projections of space curves on quadrics, utilizing cohomological methods to address longstanding problems in algebraic geometry.

## Contribution

It introduces new techniques for studying cuspidal projections of space curves on quadrics, advancing understanding of injective morphisms and singularities in algebraic geometry.

## Key findings

- Characterization of cuspidal projections on quadrics
- Use of cohomological vanishings in linear series analysis
- Insights into singularities of projected curves

## Abstract

We study linear series on curves inducing injective morphisms to projective space, using zero-dimensional schemes and cohomological vanishings. Albeit projections of curves and their singularities are of central importance in algebraic geometry, basic problems still remain unsolved. In this note, we study cuspidal projections of space curves lying on irreducible quadrics (in arbitrary characteristic).