Search results for "Zero divisor"

showing 2 items of 2 documents

On the divisor class group of double solids

1999

For a double solid V→ℙ3> branched over a surface B⊂ℙ3(ℂ) with only ordinary nodes as singularities, we give a set of generators of the divisor class group \(\) in terms of contact surfaces of B with only superisolated singularities in the nodes of B. As an application we give a condition when H* (˜V , ℤ) has no 2-torsion. All possible cases are listed if B is a quartic. Furthermore we give a new lower bound for the dimension of the code of B.

CombinatoricsSurface (mathematics)Number theoryDivisor summatory functionGroup (mathematics)DivisorGeneral MathematicsAlgebraic geometryUpper and lower boundsZero divisorMathematicsmanuscripta mathematica
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Global 1-Forms and Vector Fields

2014

In this chapter we recall some fundamental facts concerning holomorphic 1-forms on compact surfaces: Albanese morphism, Castelnuovo–de Franchis Lemma, Bogomolov Lemma. We also discuss the logarithmic case, which is extremely useful in the study of foliations with an invariant curve. Finally we recall the classification of holomorphic vector fields on compact surfaces. All of this is very classical and can be found, for instance, in [2, Chapter IV] and 24, 35].

Pure mathematicsMathematics::Algebraic GeometryMorphismLogarithmHolomorphic functionKodaira dimensionVector fieldInvariant (mathematics)Zero divisorHirzebruch surfaceMathematics
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