Cox ring of the generic fiber

Antonio Laface; Luca Ugaglia

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arXiv · 1708.02797

Cox ring of the generic fiber

Antonio Laface·Luca Ugaglia

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Abstract

Given a surjective morphism $\pi\colon X\to Y$ of normal varieties satisfying some regularity hypotheses we prove how to recover a Cox ring of the generic fiber of $\pi$ from the Cox ring of $X$. As a corollary we show that in some cases it is also possible to recover the Cox ring of a very general fiber, and finally we give an application in the case of the blowing-up of a toric fiber space.

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Antonio Laface, Luca Ugaglia. 2017-08-09. Cox ring of the generic fiber. https://arxiv.org/abs/1708.02797

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