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A fansy divisor on M_{0,n}
Klaus Altmann,Georg Hein +1 more
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In this paper, the Grassmannian Grass(2,n) is presented as a fansy divisor on the moduli space of stable, n-pointed, rational curves.Abstract:
We study the relation between projective T-varieties and their affine cones in the language of the so-called divisorial fans and polyhedral divisors. As an application, we present the Grassmannian Grass(2,n) as a ``fansy divisor'' on the moduli space of stable, n-pointed, rational curves.read more
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Book ChapterDOI
The Geometry of T-Varieties
TL;DR: A survey of polyhedral divisors describing T-varieties is given in this paper, in parallel to the well established the-ory of toric varieties, including singularities, separatedness, properness, intersection theory, cohomology, Cox rings, polarizations, and equivariant deformations.
Journal ArticleDOI
Polarized Complexity-One T-Varieties
Nathan Ilten,Hendrik Süß +1 more
TL;DR: In this paper, the authors describe polarized complexity-one T-varieties combinatorially in terms of so-called divisorial polytopes, and show how geometric properties of such a variety can be read off the corresponding polytope.
BookDOI
The Geometry of T-Varieties
TL;DR: A survey of polyhedral divisors describing T-varieties is given in this paper, which is explained in parallel to the well established theory of toric varieties, including singularities, separatedness and properness, intersection theory, cohomology, Cox rings, polarizations and equivariant deformations.
Journal ArticleDOI
Upgrading and downgrading torus actions
Nathan Ilten,Robert Vollmert +1 more
TL;DR: In this article, Altmann and Hausen have shown that affine T -varieties can be described in terms of p-divisors, and they gave explicit constructions for the p-Divisors describing certain Cox rings.
Journal ArticleDOI
On torus actions of higher complexity
TL;DR: In this article, the authors systematically produce algebraic varieties with torus action by constructing them as suitably embedded subvarieties of toric varieties, which admit an explicit treatment in terms of algebraic geometry and graded ring theory.
References
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Book
Representation Theory: A First Course
TL;DR: This volume represents a series of lectures which aims to introduce the beginner to the finite dimensional representations of Lie groups and Lie algebras.
OtherDOI
Chow quotients of Grassmannians. I
TL;DR: In this article, a certain compactification of the space of projective configurations is introduced by considering limit position (in the Chow variety) of the closures of generic orbits, which differs considerably from Mumford's geometric invariant theory quotient.
Journal ArticleDOI
Polyhedral divisors and algebraic torus actions
Klaus Altmann,Juergen Hausen +1 more
TL;DR: In this article, a complete description of normal affine varieties with effective algebraic torus action in terms of what we call proper polyhedral divisors on semiprojective varieties is provided.
Journal ArticleDOI
Quotients of toric varieties
Posted Content
Polyhedral Divisors and Algebraic Torus Actions
Klaus Altmann,Juergen Hausen +1 more
TL;DR: In this paper, a complete description of normal affine varieties with effective algebraic torus action in terms of what we call proper polyhedral divisors on semiprojective varieties is provided.