Given a surjective morphism π:X→Y of normal varieties satisfying some regularity hypotheses we prove how to recover a Cox ring of the generic fiber of π 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.
Laface A., Ugaglia L. (2020). Cox ring of the generic fiber. JOURNAL OF ALGEBRA, 551, 191-208 [10.1016/j.jalgebra.2020.01.013].
Cox ring of the generic fiber
Ugaglia L.
2020-01-01
Abstract
Given a surjective morphism π:X→Y of normal varieties satisfying some regularity hypotheses we prove how to recover a Cox ring of the generic fiber of π 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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