Good quotients of Mori dream spaces
Hendrik B\"aker
TL;DR
This paper proves that taking good quotients of algebraic varieties with finitely generated Cox rings results in new varieties that also have finitely generated Cox rings, preserving this property under quotients.
Contribution
It establishes that good quotients of Mori dream spaces retain the property of having finitely generated Cox rings, extending the class of Mori dream spaces.
Findings
Good quotients preserve finite generation of Cox rings.
Mori dream spaces remain Mori dream spaces after good quotients.
The property of being a Mori dream space is stable under good quotients.
Abstract
We show that good quotients of algebraic varieties with finitely generated Cox ring have again finitely generated Cox ring.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Polynomial and algebraic computation