Syzygies of Line Bundles on GIT Quotients

Krishna Hanumanthu; Anwesh Ray

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arXiv · 1509.00341

Syzygies of Line Bundles on GIT Quotients

Krishna Hanumanthu·Anwesh Ray

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Abstract

Let $k$ be an algebraically closed field. Consider a reductive group $G$ over $k$. Let $X$ be a projective variety over $k$ with a $G$-action and let $L$ be a very ample $G$-linearized line bundle on $X$. Suppose that $L$ descends to the GIT quotient of $X$ by $G$. If $L$ satisfies the property $N_p$ one can ask if its descent also has $N_p$ property. In this article, we show this is the case under certain conditions. We then apply our results to some cases of interest. As a consequence of our results, we show that if $G$ is a finite group and $L$ satisfies $N_p$ property and its descent satisfies $N_0$ property then it satisfies $N_p$ property as well under suitable conditions.

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BibTeX RIS

Krishna Hanumanthu, Anwesh Ray. 2016-02-22. Syzygies of Line Bundles on GIT Quotients. https://arxiv.org/abs/1509.00341

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