On the divisor class group of double solids

Details On the divisor class group of double solids On the divisor class group of double solids

1998-09-28

arxiv.org/abs/math/9809158v2

Mathematics

Algebraic Geometry

16 pages, minor grammatical changes

Scientific paper

For a double solid $V\to P_3(C)$ branched over a surface $B\subset P_3(C)$ with only ordinary nodes as singularities, we give a set of generators of the divisor class group $Pic(\tilde{V}})$ in terms of contact surfaces of $B$ with only superisolated singularities in the nodes of $B$. As an application we give a condition when the integral cohomology of $\tilde{V}$ has no 2-torsion. All possible cases are listed if $B$ is a quartic surface. Furthermore we give a new lower bound for the dimension of the code of $B$.

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