Let phi: X -> Y be a map of Q-factorial Mori dream spaces. We prove that there is a unique Cox lift Phi: 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 phi is induced from 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.
Maps of Mori dream spaces / A. Hochenegger, E. Martinengo. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 222:6(2018 Jun), pp. 1287-1305. [10.1016/j.jpaa.2017.06.018]
Maps of Mori dream spaces
A. Hochenegger
Primo
;
2018
Abstract
Let phi: X -> Y be a map of Q-factorial Mori dream spaces. We prove that there is a unique Cox lift Phi: 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 phi is induced from 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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