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arXiv · alg-geom/9708023

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

Hirotachi Abo·Wolfram Decker·Nobuo Sasakura
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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.

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Hirotachi Abo, Wolfram Decker, Nobuo Sasakura. 1997-08-28. An elliptic conic bundle in P^4 arising from a stable rank-3 vector bundle. https://arxiv.org/abs/alg-geom/9708023

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