Let be a map of -factorial Mori dream spaces. We prove that there is a unique Cox lift of Mori dream stacks coming from a homogeneous homomorphism , where is a canonical stack of Y and 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.
Maps of Mori dream spaces
Elena Martinengo;
2018-01-01
Abstract
Let be a map of -factorial Mori dream spaces. We prove that there is a unique Cox lift of Mori dream stacks coming from a homogeneous homomorphism , where is a canonical stack of Y and 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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