Effective de Rham Cohomology - The Hypersurface Case

Details Effective de Rham Cohomology - The Hypersurface Case Effective de Rham Cohomology - The Hypersurface Case

2011-12-12

arxiv.org/abs/1112.2489v3

Mathematics

Algebraic Geometry

6 pages, proof of Lemma 1 was unclear, main result now proved without it; bound slightly changed

Scientific paper

We prove an effective bound for the degrees of generators of the algebraic de Rham cohomology of smooth affine hypersurfaces. In particular, we show that the de Rham cohomology H_dR^p(X) of a smooth hypersurface X of degree d in C^n can be generated by differential forms of degree d^O(pn). This result is relevant for the algorithmic computation of the cohomology, but is also motivated by questions in the theory of ordinary differential equations related to the infinitesimal Hilbert 16th problem.

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