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

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

1997-08-28

arxiv.org/abs/alg-geom/9708023v1

Mathematics

Algebraic Geometry

13 pages, AmS-TeX v. 2.1

Scientific paper

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.

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