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arXiv · 1904.04944

Asymptotic Syzygies in the Setting of Semi-Ample Growth

Juliette Bruce
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Abstract

We study the asymptotic non-vanishing of syzygies for products of projective spaces. Generalizing the monomial methods of Ein, Erman, and Lazarsfeld \cite{einErmanLazarsfeld16} we give an explicit range in which the graded Betti numbers of $\mathbb{P}^{n_1}\times \mathbb{P}^{n_2}$ embedded by $\mathcal{O}_{\mathbb{P}^{n_1}\times\mathbb{P}^{n_2}}(d_1,d_2)$ are non-zero. These bounds provide the first example of how the asymptotic syzygies of a smooth projective variety whose embedding line bundle grows in a semi-ample fashion behave in nuanced and previously unseen ways.

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Juliette Bruce. 2019-04-09. Asymptotic Syzygies in the Setting of Semi-Ample Growth. https://arxiv.org/abs/1904.04944

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