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arXiv · 1407.8491

Non-reduced components of the Noether-Lefschetz locus

Ananyo Dan
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Abstract

For a fixed integer $d \ge 5$, the Noether-Lefschetz locus parametrizes smooth degree $d$ complex hypersurfaces in $\mathbb{P}^3$ with Picard number greater than $1$. There are infinitely many irreducible components of this locus. The aim of this article is to understand the scheme structure of these components. In particular, we study when is such a component non-reduced. We give a criterion for such a component to be non-reduced. Finally, we give examples of such components.

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Ananyo Dan. 2014-07-31. Non-reduced components of the Noether-Lefschetz locus. https://arxiv.org/abs/1407.8491

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