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.
Settore MAT/03 - Geometria
Laface A., Ugaglia L. (2020). Cox ring of the generic fiber. JOURNAL OF ALGEBRA, 551, 191-208 [10.1016/j.jalgebra.2020.01.013].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/413236
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