Maps of Mori dream spaces

Abstract

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.

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

“…Similar statement for regular maps between ℚ-factorial Mori Dream Spaces has been independently obtained by Andreas Hochenegger and Elena Martinengo [10]. Their approach is to use the language of Mori Dream stacks [11].…”

Cox rings and algebraic maps

“…The main tool that will be used in the proofs of Theorems and is the following result from . Theorem Let X and Y be Mori Dream Spaces with the Cox rings R and S , respectively.…”

“…The main tool that will be used in the proofs of Theorems 3.2 and 3.5 is the following result from [10].…”