Compactifications of subvarieties of tori
By Jenia Tevelev. 2004
242 citations recorded by the source corpus.
We study compactifications of subvarieties of algebraic tori defined by imposing a sufficiently fine polyhedral structure on their non-archimedean amoebas. These compactifications have many nice properties, for example any k boundary divisors intersect in codimension k. We consider some examples including M0,n ⊂ M0,n (and more generally log canonical models of complements of hyperplane arrangements) and compact quotients of Grassmannians by a maximal torus.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/10d0e4d9c344cb62b4022aee81c06b12fdfc6df0
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In Discrete Mathematics and Combinatorics
- Eric Katz
- June Huh
- Martin Ulirsch
- A. Gibney
- Diane Maclagan
- Bernd Sturmfels
- Jenia Tevelev
- Dhruv Ranganathan
In Geometry and Topology
- Eric Katz
- Bernd Sturmfels
- Jenia Tevelev
- Martin Ulirsch
- Dhruv Ranganathan
- June Huh
- A. Gibney
- Diane Maclagan
Citations in the corpus
- Equations for Chow and Hilbert quotients (2007, methodology): “This exhibits M0,n as a hyperplane complement and as a very affine variety in its intrinsic torus [Tevelev 2007].”
- A Tropical Toolkit (2006, background): “The second part is a foundational account of tropical intersection theory with proofs of some new theorems relating it to classical intersection theory.”
- Log-concavity of characteristic polynomials and the Bergman fan of matroids (2011, background): “2 of [23] states that Y intersects torus orbits of X properly iff Trop(Y ◦) is a union of cones of .”
- Functorial tropicalization of logarithmic schemes: the case of constant coefficients (2013, methodology): “Moreover, the further results of [49] show that one can use the polyhedral geometry of TropX(Y ) to study properties of Y , thought of as a partial embedded compactification of Y0 = Y ∩X, expanding on Tevelev’s theory of tropical compactifications (see [46]).”
- Stable pair, tropical, and log canonical compactifications of moduli spaces of del Pezzo surfaces (2007, background): “ments on ball quotients, by Kond¯ o, Dolgachev, Heckman, Looijenga and others. See [ 35 ] and the references there.”