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Morphisms from Quintic Threefolds to Cubic Threefolds are Constant

David Sheppard
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Abstract

We show that every morphism from a degree 5 hypersurface in 4-dimensional projective space to a nonsingular degree 3 hypersurface in 4-dimensional projective space is necessarily constant. In the process, we also classify morphisms from the projective plane to nonsingular cubic threefolds given by degree 3 polynomials.

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David Sheppard. 2003-01-31. Morphisms from Quintic Threefolds to Cubic Threefolds are Constant. https://arxiv.org/abs/math/0302006

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