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arXiv · 2510.03036

Very ample line bundles on weighted projective spaces and weighted blowups

Stevell Muller·Erik Paemurru
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Abstract

We consider line bundles $\mathcal{O}(kd)$ on weighted projective spaces, where $k$ is an integer and $d$ is the least common multiple of the weights. Such line bundles are ample if and only if $k$ is positive. On the other hand, determining which line bundles are very ample is a delicate problem. We give various sharp criteria for very ampleness. As an example, if the weights are pairwise coprime, then $\mathcal{O}(d)$ is always very ample, which implies that general smooth well-formed weighted hypersurfaces of dimension at least two are simply connected. We also treat weighted blowups, relative very ampleness, projective normality, Rees rings and generation in degree 1 of Veronese subrings.

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Stevell Muller, Erik Paemurru. 2026-08-06. Very ample line bundles on weighted projective spaces and weighted blowups. https://arxiv.org/abs/2510.03036

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