Zur Erinnerung an Clemens Winkler

Aertsen and Clemens Boucsein

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Clemens ’ Conjecture : Part I

This is the first of a series of two papers: Clemens’ conjecture: part I, Clemens’ conjecture: part II. In these two papers we solve the Clemens’ conjecture: there are finitely many smooth rational curves of each degree in a generic quintic threefold. In this paper, we deal with a family of smooth Calabi-Yau threefolds fǫ for a small complex number ǫ. If fǫ contains a smooth rational curve cǫ, ...

Clemens ’ S Conjecture : Part I

This is the first of a series of two papers in which we solve the Clemens conjecture: there are only finitely many smooth rational curves of each degree in a generic quintic threefold. In this paper, we deal with a family of smooth Calabi-Yau threefolds fǫ for a small complex number ǫ. If fǫ contains a smooth rational curve cǫ, then its normal bundle is Ncǫ (fǫ) = Ocǫ (k) ⊕ Ocǫ (−2− k) for k ≥ ...

On a Conjecture of Clemens

Clemens has conjectured that a generic sextic threefold contains no rational curves. Here we prove a generalization of this conjecture, in the form of effectivity of a certain twist of the canonical bundle of a codimension-2 subvariety of a generic hypersurface in an arbitrary ambient variety. The geometry of a desingularization Y m of an arbitrary subvariety of a generic hypersurface X n in an...

Inelastic Charged - Lepton Scattering off Nucleons * _ Clemens