English

An elliptic conic bundle in P^4 arising from a stable rank-3 vector bundle

alg-geom 2009-09-25 v1 Algebraic Geometry

Abstract

In this note we show the existence of a family of elliptic conic bundles in P^4 of degree 8. This family has been overlooked and in fact falsely ruled out in a series of classification papers. Our surfaces provide a counterexample to a conjecture of Ellingsrud and Peskine. According to this conjecture there should be no irregular m-ruled surface in P^4 for m at least 2.

Keywords

Cite

@article{arxiv.alg-geom/9708023,
  title  = {An elliptic conic bundle in P^4 arising from a stable rank-3 vector bundle},
  author = {Hirotachi Abo and Wolfram Decker and Nobuo Sasakura},
  journal= {arXiv preprint arXiv:alg-geom/9708023},
  year   = {2009}
}

Comments

13 pages, AmS-TeX v. 2.1

R2 v1 2026-07-22T07:42:46.417Z