Enriques surfaces of non-degeneracy 3

TL;DR

This paper classifies certain sequences of half-fibers on Enriques surfaces and proves that, in characteristic not 2, all such surfaces admit a 4-sequence, linking them to specific algebraic models.

Contribution

It provides a complete classification of non-extendable 3-sequences on Enriques surfaces and establishes the existence of 4-sequences in characteristic not 2, connecting surfaces to well-known algebraic models.

Findings

All non-extendable 3-sequences classified

Every Enriques surface admits a 4-sequence in characteristic ≠ 2

Enriques surfaces are birational to Castelnuovo quintics

Abstract

We classify all non-extendable 3-sequences of half-fibers on Enriques surfaces. If the characteristic is different from 2, we prove in particular that every Enriques surface admits a 4-sequence, which implies that every Enriques surface is the minimal desingularization of an Enriques sextic, and that every Enriques surface is birational to a Castelnuovo quintic.