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Canonical bases for cluster algebras

- M. Gross, P. Hacking, S. Keel, M. Kontsevich
- Mathematics
- 5 November 2014

In [GHK11], Conjecture 0.6, the first three authors conjectured that the ring of regular functions on a natural class of affine log Calabi-Yau varieties (those with maximal boundary) has a canonical… Expand

Mori dream spaces and GIT.

The main goal of this paper is to study varieties with the best possible Mori theoretic properties (measured by the existence of a certain decomposition of the cone of effective divisors). We call… Expand

Intersection theory of moduli space of stable N-pointed curves of genus zero

- S. Keel
- Mathematics
- 1 February 1992

We give a new construction of the moduli space via a composition of smooth codimension two blowups and use our construction to determine the Chow ring

Quotients by Groupoids

We show that if a flat group scheme acts properly, with finite stabilizers, on an algebraic space, then a quotient exists as a separated algebraic space. More generally we show any flat groupid for… Expand

Mirror symmetry for log Calabi-Yau surfaces I

- M. Gross, P. Hacking, S. Keel
- Mathematics
- 24 June 2011

We give a canonical synthetic construction of the mirror family to pairs (Y,D) where Y is a smooth projective surface and D is an anti-canonical cycle of rational curves. This mirror family is… Expand

Basepoint freeness for nef and big line bundles in positive characteristic

- S. Keel
- Mathematics
- 1 January 1999

A necessary and sufficient condition is given for semi-ampleness of a numerically effective (nef) and big line bundle in positive characteristic. One application is to the geometry of the universal… Expand

Towards the ample cone of \overline{}_{,}

- A. Gibney, S. Keel, I. Morrison
- Mathematics
- 27 June 2000

In this paper we study the ample cone of the moduli space $\mgn$ of stable $n$-pointed curves of genus $g$. Our motivating conjecture is that a divisor on $\mgn$ is ample iff it has positive… Expand

Rational curves on quasi-projective surfaces

- S. Keel, J. McKernan
- Mathematics
- 25 July 1997

Introduction and statement of results Glossary of notation and conventions Gorenstein del Pezzo surfaces Bug-eyed covers Log deformation theory Criteria for log uniruledness Reduction to… Expand

Birational geometry of cluster algebras

- M. Gross, P. Hacking, S. Keel
- Mathematics
- 10 September 2013

We give a geometric interpretation of cluster varieties in terms of blowups of toric varieties. This enables us to provide, among other results, an elementary geometric proof of the Laurent… Expand

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