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.

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.

Maps of Mori dream spaces

Hochenegger A.
;
2018

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.
2018
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/95428
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