Surfaces elliptiques réelles et inégalité de Ragsdale-Viro

Details Surfaces elliptiques réelles et inégalité de Ragsdale-Viro Surfaces elliptiques réelles et inégalité de Ragsdale-Viro

1998-07-03

arxiv.org/abs/math/9807020v1

Mathematics

Algebraic Geometry

AmSTeX with amsppt.sty and psfig.sty, 11 pages, 2 figures

Scientific paper

On a real regular elliptic surface without multiple fiber, the Betti number $h_1$ and the Hodge number $h^{1,1}$ are related by $h_1\leq h^{1,1}$. We prove that it's always possible to deform such algebraic surface to obtain $h_1=h^{1,1}$. Furthermore, we can impose that each homology class can be represented by a real algebraic curve. We use a real version of the modular construction of elliptic surfaces.

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