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Showing 1 to 20 of 75 for “"toric"”.
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Folded Symplectic Toric Four -Manifolds
… map, the manifold is called a folded symplectic toric manifold. Motivated by results in symplectic geometry, our goal is to prove a classification theorem of folded symplectic toric manifolds. This work is a step in that direction: the main result is a necessary and sufficient condition for two …
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Toric Varieties Associated with Moduli Spaces
… to study the cohomology of associated toric varieties. While we are able to make use of the work of Danilov to obtain the integral (rational) cohomology ring in the smooth (orbifold) case, we show that the aforementioned toric varieties almost always possess singularities worse than …
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Four Dimensional Toric Orbifolds and Holography
L'abstract è presente nell'allegato / the abstract is in the attachment
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Equivariant Index on Toric Contact Manifolds
Let (M, D, G) be a (2n + 1)-dimensional toric contact manifold of Reeb type with moment cone C, where n > 1. There exists a G-invariant Sasakian 1-form on M such that D = ker α. This structure allows us to define the horizontal Dolbeault operator on M and more generally the horizontal Dolbeault …
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Toric mirror symmetry and GIT windows
… joint work [HZ20], studies mirror symmetry for toric varieties from the perspective of geometric invariant theory. We translate GIT constructions of toric varieties into skeletal terms and study them in the context of wrapped Fukaya categories and wrapped constructible sheaves. We explain how …
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Real, complex and quaternionic toric spaces
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1993.
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Descent Systems, Eulerian Polynomials and Toric Varieties
… give the Betti numbers for certain smooth toric varieties associated with the permutohedra. In this thesis we derive recurrences for the h-vectors of a family of polytopes generalizing this. The simple polytopes we consider arise as the orbit of a non-generic weight, namely a weight fixed …
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A classification of toric, folded-symplectic manifolds
Given a $G$-toric, folded-symplectic manifold with co-orientable folding hypersurface, we show that its orbit space is naturally a manifold with corners $W$ equipped with a smooth map $\psi: W \to \frak{g}^*$, where $\frak{g}^*$ is the dual of the Lie algebra of the torus, $G$. The map $\psi$ has …
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Fibered Calabi -Yau Varieties and Toric Varieties
… to write weighted projective space bundles as toric varieties. We then find necessary and sufficient conditions for the anti-canonical linear systems of these bundles to have quasi-smooth members. These quasi-smooth members are Calabi-Yau varieties over the base whose general fiber is also a …
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Symplectic toric stratified spaces with isolated singularities
We provide a classification of two types of toric objects: symplectic toric cones and symplectic toric stratified spaces with isolated singularities. Both types of object are classified via orbital moment map and a second degree cohomology class. As symplectic toric stratified spaces with isolated …
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Mirrors to Toric Degenerations via Intrinsic Mirror Symmetry
… constructions in Gross-Siebert mirror symmetry: toric degeneration mirror symmetry and intrinsic mirror symmetry. After briefly exploring the case of degenerations of elliptic curves, we show that the Gross-Siebert mirror construction for minimal relative log Calabi-Yau degenerations generalizes …
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The intersection homology with twisted coefficients of toric varieties
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1991.
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Delzant-type classification of near-symplectic toric 4-manifolds
Delzant's theorem for symplectic toric manifolds says that there is a one-to-one correspondence between certain convex polytopes in ... and symplectic toric 2n-manifolds, realized by the image of the moment map. I present proofs of this theorem and the convexity theorem of …
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Characteristics cycles of toric varieties : perverse sheaves on rank stratifications
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1995.
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The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds
… collection of algebraic topological results for toric origami manifolds, mostly in dimension 4. Using a known formula for the fundamental group of a compact orientable toric origami manifold, a list of all groups obtainable as the fundamental group of a compact orientable toric origami 4-manifold …
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Properties of the Toric Rings of a Chordal Bipartite Family of Graphs
… of a group of Koszul algebras coming from the toric ideals of a chordal bipartite infinite family of graphs (alternately, these rings may be interpreted as coming from determinants of certain ladder-like structures). We determine a linear system of parameters for each ring and explicitly …
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Elliptic fibrations among toric hypersurface Calabi-Yau manifolds and mirror symmetry of fibrations
… of elliptic and genus one fibrations among toric hypersurface Calabi-Yau three folds by (1) constructing explicitly elliptically fibered Calabi-Yau threefolds with large Hodge numbers using Weierstrass model techniques motivated by F-theory, and comparing the Tate-tuned Wierstrass model set …
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On the Quantum Cohomology of Fano Toric Manifolds and the Intersection Cohomology of Singular Symplectic Quotients
The second result computes the intersection cohomology of the singular symplectic reduced spaces. Let M be a closed symplectic manifold with a Hamiltonian S1-action defined on it and mu is the moment map. If 0 is a singular value of mu, the reduced space mu-1(0)/S1 is, in general, no longer an …
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