Related papers: Mirror Principle For Flag Manifolds
The SYZ conjecture suggests a folklore that "Lagrangian multi-sections are mirror to holomorphic vector bundles". In this paper, we prove this folklore for Lagrangian multi-sections inside the cotangent bundle of a vector space, which are…
For any triple of positive integers $A' = (a_1',a_2',a_3')$ and $c \in \mathbb{C}^*$, cusp polynomial $f_{A'} = x_1^{a_1'}+x_2^{a_2'}+x_3^{a_3'}-c^{-1}x_1x_2x_3$ is known to be mirror to Geigle-Lenzing orbifold projective line…
T-duality acts on circle bundles by exchanging the first Chern class with the fiberwise integral of the H-flux, as we motivate using E_8 and also using S-duality. We present known and new examples including NS5-branes, nilmanifolds, Lens…
Applying the technique of $p$-adic integration, we prove the topological mirror symmetry conjecture of Hausel-Thaddeus for the moduli spaces of (strongly) parabolic Higgs bundles for the structure groups $\text{SL}_n$ and $\text{PGL}_n$,…
We determine the minimal equivariant embedding dimension of orthgonal groups acting on real flag manifolds and unitary groups acting on complex flag manifolds. The minimal embedding dimension is achieved at isospectral model.
This paper discusses consistent flag bicolorings of maps and maniplexes, in their own right and as generalizations of orientations and pseudo-orientations. Furthermore, a related doubling concept is introduced, and relationships between…
Mirror symmetry suggests that on a Calabi-Yau 3-fold moduli spaces of stable bundles, especially those with degree zero and indivisible Chern class, might be smooth (i.e. unobstructed, though perhaps of too high a dimension). This is…
We prove a result of Chern-Weil type for canonically metrized line bundles on one-parameter families of smooth complex curves. Our result generalizes a result due to J.I. Burgos Gil, J. Kramer and U. K\"uhn that deals with a line bundle of…
We present here the K-theoretic version of mirror models of toric manifold. First, we recall the construction of cohomological mirrors for toric manifolds, i.e. representations of the toric hypergeometric functions from quantum cohomology…
The aim of this paper is to describe the equivariant and ordinary Grothendieck ring and the equivariant and ordinary topological $K$-ring of flag Bott manifolds of general Lie type. This will generalize the results on the equivariant and…
We introduce self-dual manifolds and show that they can be used to encode mirror symmetry for affine-K\"{a}hler manifolds and for elliptic curves. Their geometric properties, especially the link with special lagrangian fibrations and the…
We derive conjectures, called genus 1 Enumerative mirror symmetry for moduli spaces of Higgs bundles, which relate curve-counting invariants of moduli spaces of Higgs $\mathrm{SL}_r$-bundles to curve-counting invariants of moduli spaces of…
A simple algebraic characterization of the Fano manifolds in the class of homogeneous toric bundles over a flag manifold $G^C/P$ is provided in terms of symplectic data.
We give geometric explanations and proofs of various mirror symmetry conjectures for $T^{n}$-invariant Calabi-Yau manifolds when instanton corrections are absent. This uses fiberwise Fourier transformation together with base Legendre…
We generalise partial results about the Yau-Tian-Donaldson correspondence on ruled manifolds to bundles whose fibre is a classical flag variety. This is done using Chern class computations involving the combinatorics of Schur functors. The…
We present the new explicit geometrical knowledge of the Landau-Ginzburg orbifolds, when a typical type of superpotential is considered. Relying on toric geometry, we show the one-to-one correspondence between some of the $(a,c)$ states…
A flag manifold over a semifield K can be partitioned into "half i-circles" which are orbits of a K-action on that flag manifold. Here i is fixed and it corresponds to a simple reflection in the Weyl group. We prove (for certain K) a…
Let $X$ be Calabi-Yau manifold acted by a group $G$. We give a definition of $G$-equivariance for branes on $X$, and assign to each equivariant brane an element of the equivariant cohomology of $X$ that can be considered as a charge of the…
We prove that the tangent bundle of a generic space of planar n-gons with specified side lengths, identified under isometry, plus a trivial line bundle is isomorphic to (n-2) times a canonical line bundle. We then discuss consequences for…
In this paper we will describe an approach to mirror symmetry for appropriate 1-dimensional DM stacks of arithmetic genus $g \leq 1$, called tcnc curves, which was developed by the author with Treumann and Zaslow in arXiv:1103.2462 . This…