Book contents
- Frontmatter
- Dedicaton
- Contents
- Contributors
- Happy Birthday
- On Stable Cohomology of Central Extensions of Elementary Abelian Groups
- On Projective 3-Folds of General Type with pg = 2
- 15-Nodal Quartic Surfaces. Part I: Quintic del Pezzo Surfaces and Congruences of Lines in P3
- Mori Flips, Cluster Algebras and Diptych Varieties Without Unprojection
- The Mirror of the Cubic Surface
- Semi-Orthogonal Decomposition of a Derived Category of a 3-Fold With an Ordinary Double Point
- Duality and Normalization, Variations on a Theme of Serre and Reid
- Rationality of Q-Fano Threefolds of Large Fano Index
- An Exceptional Locus in the Perfect Compactification of Ag
- Variation of Stable Birational Types of Hypersurfaces
- Triangle Varieties and Surface Decomposition of Hyper-Käahler Manifolds
- References
Mori Flips, Cluster Algebras and Diptych Varieties Without Unprojection
Published online by Cambridge University Press: 25 October 2022
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Book contents
- Frontmatter
- Dedicaton
- Contents
- Contributors
- Happy Birthday
- On Stable Cohomology of Central Extensions of Elementary Abelian Groups
- On Projective 3-Folds of General Type with pg = 2
- 15-Nodal Quartic Surfaces. Part I: Quintic del Pezzo Surfaces and Congruences of Lines in P3
- Mori Flips, Cluster Algebras and Diptych Varieties Without Unprojection
- The Mirror of the Cubic Surface
- Semi-Orthogonal Decomposition of a Derived Category of a 3-Fold With an Ordinary Double Point
- Duality and Normalization, Variations on a Theme of Serre and Reid
- Rationality of Q-Fano Threefolds of Large Fano Index
- An Exceptional Locus in the Perfect Compactification of Ag
- Variation of Stable Birational Types of Hypersurfaces
- Triangle Varieties and Surface Decomposition of Hyper-Käahler Manifolds
- References
Summary
We give a survey on the connections between terminal 3-fold flips and cluster algebras. In particular we observe that Mori’s algorithm for generating the relations defining a type k2A flipping neighbourhood is a form of generalised cluster algebra mutation. We then use the Laurent phenomenon for this cluster algebra structure to give an alternative proof of the existence of Brown and Reid’s diptych varieties.
- Type
- Chapter
- Information
- Recent Developments in Algebraic GeometryTo Miles Reid for his 70th Birthday, pp. 116 - 149Publisher: Cambridge University PressPrint publication year: 2022
References
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