An elliptic conic bundle in P⁴ arising from a stable rank-3 vector bundle

1997/08/28 by Hirotachi Abo, Abo, Hirotachi, Wolfram Decker +3 · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.alg-geom/9708023

Abstract

In this note we show the existence of a family of elliptic conic bundles in P⁴ 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 P⁴ for m at least 2.

Cited by

• Horrocks theory and the Bernstein-Gelfand-Gelfand correspondence
• On The Projective Normality of Smooth Surfaces of degree nine

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