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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/151641
Divisors of bielliptic surfaces and embeddings in p4
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Abstract
Bielliptic surfaces (also called "hyperelliptic surfaces") are defined to be minimal algebraic
surf aces of Kodaira dimension O and irregularity 1. They play a special role in the birational classification
of surfaces. The first part of this paper gives an explicit description of the cohomology group H 2(S, Z)
for a bielliptic surface S. In the second part the author proves the existence of smooth bielliptic surfaces
in P4 • The proof relies on Reider's criterion for very-ampleness. In fact, a complete characterization of
polarized bielliptic surfaces in P4 is given. These surfaces add to the very short list of known irregular surfaces in P4 , the other two being the abelian surfaces of Horrocks-Mumford and the elliptic quintic
scrolls.
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Preprint enviat per a la seva publicació en una revista científica: Mathematische Zeitschrift. 1990, Vol. 203, p. 527-533.
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SERRANO, Fernando. Divisors of bielliptic surfaces and embeddings in p4. [consulted: 7 of August of 2026]. Available at: https://hdl.handle.net/2445/151641