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arXiv · 2011.11069

An asymptotic Alexander-Hirschowitz theorem for surfaces

Carl Lian
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Abstract

Let X be a smooth projective surface over C and let L be an ample line bundle on X. In this note, we show that, for all sufficiently large d, any number of general double points on X imposes the expected number of conditions on the linear system |L^d|. Equivalently, the space of d-plane sections of X singular at any number of general points has the expected dimension. We conjecture that the same holds for X of arbitrary dimension.

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Carl Lian. 2020-11-22. An asymptotic Alexander-Hirschowitz theorem for surfaces. https://arxiv.org/abs/2011.11069

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