Results 21 to 30 of about 120 (44)
On the finite generation of valuation semigroups on toric surfaces
, 2023 We provide a combinatorial criterion for the finite generation of a valuation semigroup associated with an ample divisor on a smooth toric surface and a non-toric valuation of maximal rank.
Altmann, Klaus +4 more
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Crystal bases and Newton-Okounkov bodies
, 2015 Let G be a connected reductive algebraic group. We prove that the string parametrization of a crystal basis for a finite dimensional irreducible representation of G extends to a natural valuation on the field of rational functions on the flag variety G/B,
Kaveh, Kiumars
core +1 more source
Mixed volume and an extension of intersection theory of divisors [PDF]
, 2010 Let K(X) be the collection of all non-zero finite dimensional subspaces of rational functions on an n-dimensional irreducible variety X. For any n-tuple L_1,..., L_n in K(X), we define an intersection index [L_1,..., L_n] as the number of solutions in X ...
Kaveh, Kiumars, Khovanskii, A. G.
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Fano Varieties and Fano Polytopes [PDF]
, 2020 The foundation of this thesis is the problem whether a given (normal) Gorenstein Fano variety can be degenerated to a toric Gorenstein Fano variety. We will only consider those degenerations that are compatible with the choice of an ample line bundle on ...
Steinert, Christian Pascal
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Overdetermined Systems of Equations on Toric, Spherical, and Other Algebraic Varieties
, 2020 Let $E_1,\ldots,E_k$ be a collection of linear series on an algebraic variety $X$ over $\mathbb{C}$. That is, $E_i\subset H^0(X, \mathcal{L}_i)$ is a finite dimensional subspace of the space of regular sections of line bundles $ \mathcal{L}_i$.
Monin, Leonid
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Monomial bases and PBW filtration in representation theory [PDF]
, 2016 In this thesis we study the Poincaré–Birkhoff–Witt (PBW) filtration on simple finite-dimensional modules of simple complex finite-dimensional Lie algebras.
Backhaus, Teodor
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Toric degenerations of cluster varieties and cluster duality
, 2019 We introduce the notion of a $Y$-pattern with coefficients and its geometric counterpart: a cluster $\mathcal{X}$-variety with coefficients. We use these constructions to build a flat degeneration of every skew-symmetrizable specially completed cluster $\
Bossinger, Lara +3 more
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Dimer Models from Mirror Symmetry and Quivering Amoebae [PDF]
, 2005 Dimer models are 2-dimensional combinatorial systems that have been shown to encode the gauge groups, matter content and tree-level superpotential of the world-volume quiver gauge theories obtained by placing D3-branes at the tip of a singular toric ...
Feng, Bo +3 more
core +2 more sources
K-orbit closures and Barbasch-Evens-Magyar varieties
, 2018 We define the Barbasch-Evens-Magyar variety. We show it is isomorphic to the smooth variety defined in [D. Barbasch-S. Evens '94] that maps finite-to-one to a symmetric orbit closure, thereby giving a resolution of singularities in certain cases.
Escobar, Laura +2 more
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Arithmetic geometry of toric varieties. Metrics, measures and heights
, 2014 We show that the height of a toric variety with respect to a toric metrized line bundle can be expressed as the integral over a polytope of a certain adelic family of concave functions.
Gil, José Ignacio Burgos +2 more
core