A very short proof of the Borisov-Nuer conjecture

Matthew Dawes

A very short proof of the Borisov-Nuer conjecture

Algebraic Geometry 2019-07-24 v2 Number Theory

Authors: Matthew Dawes

Abstract

We prove a conjecture of Borisov and Nuer, which states that every element in the even unimodular lattice of signature (1,9) can be expressed as the difference of two elements of squared length -2. As a consequence, every unnodal Enriques surface admits an Ulrich line bundle.

Keywords

borisov-nuer conjecture even unimodular lattice enriques surfaces ulrich line bundle algebraic geometry

Cite

@article{arxiv.1907.04856,
  title  = {A very short proof of the Borisov-Nuer conjecture},
  author = {Matthew Dawes},
  journal= {arXiv preprint arXiv:1907.04856},
  year   = {2019}
}

Comments

Withdrawn due to a gap in the proof for the case d>0. I am grateful to Shaul Zemel for pointing this out

Related papers

View all related →