Maps of Mori Dream Spaces in Cox coordinates. Part I: existence of descriptions

Buczyński, Jarosław; Kędzierski, Oskar

doi:10.48550/arxiv.1605.06828

Cited by 3 publications

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“…Additionally, the Cox lift obtained here fulfills a certain uniqueness and can be determined quite algorithmically. Jarosław Buczyński and Oskar Kędzierski have also obtained independently a generalisation for rational maps between (even not Q-factorial) Mori dream spaces in [10]. Finally, our construction is similar in spirit to the process of destackification as introduced in [8] by Daniel Bergh. This article is organised as follows.…”

Section: Introductionmentioning

confidence: 71%

Maps of Mori dream spaces

Hochenegger

Martinengo

2018

Journal of Pure and Applied Algebra

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Abstract. Let φ : X → Y be a map of Q-factorial Mori dream spaces. We prove that there is a unique Cox lift Φ : X → Y of Mori dream stacks coming from a homogeneous homomorphism R(Y ) = R(Y) → R(X ), where Y is a canonical stack of Y and X is obtained from X by root constructions, and φ is induced from Φ by passing to coarse moduli spaces. We also apply this techniques to show that a Mori dream quotient stack is obtained by roots from its canonical stack.

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