Related papers: Canonical mirror models for maximal orthogonal Gra…

For any maximal surface group representation into $\mathrm{SO}_0(2,n+1)$, we introduce a non-degenerate scalar product on the the first cohomology group of the surface with values in the associated flat bundle. In particular, it gives rise…

There are two widely used models for the Grassmannian $\operatorname{Gr}(k,n)$, as the set of equivalence classes of orthogonal matrices $\operatorname{O}(n)/(\operatorname{O}(k) \times \operatorname{O}(n-k))$, and as the set of trace-$k$…

Motivated by Buchstaber's and Terzic' work on the complex Grassmannians G(2,4) and G(2,5) we describe the moment map and the orbit space of oriented Grassmannians of planes under the action of a maximal compact torus. Our main tool is the…

We consider the general orthogonal metric separable in space and time variables in comoving coordinates. We then characterise perfect fluid models admitted by such a metric. It turns out that the homogeneous models can only be either FLRW…

Let $R$ be a finite local ring of odd characteristic and $\beta$ a non-degenerate symmetric bilinear form on $R^2$. In this short note, we determine the largest possible cardinality of pairwise orthogonal sets of unimodular vectors in…

Let $\mathbf{LG}(V\oplus V^*)$ and $\mathbf{OG}^+(V\oplus V^*)$ denote the Lagrangian and orthogonal Grassmannians endowed with the natural $\mathbb{G}_m$-actions, respectively. Thaddeus proved that over $\mathbb{C}$, the Hilbert quotients…

The conformal transformations with respect to the metric defining $o(n,\mbb{C})$ give rise to a nonhomogeneous polynomial representation of $o(n+2,\mbb{C})$. Using Shen's technique of mixed product, we generalize the above representation to…

Let $\Sigma_g$ be a closed oriented surface of genus g and let $H_\mathbb{Q}$ denote $H_1(\Sigma_g;\mathbb{Q})$ which we understand to be the standard symplectic vector space over $\mathbb{Q}$ of dimension $2g$. We introduce a canonical…

The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric.…

Canonical metrics and conformal invariants are presented for closed oriented even-dimensional manifolds with non-degenerate conformal structures and in particular for compact Riemann surfaces.

The isotropic Grassmannian parametrizes isotropic subspaces of a vector space equipped with a quadratic form. In this paper, we show that any maximal isotropic Grassmannian in its Pl\"ucker embedding can be defined by pulling back the…

The most fundamental example of mirror symmetry compares the Fermat hypersurfaces in P^n and P^n/G, where G is a finite group that acts on P^n and preserves the Fermat hypersurface. We generalise this to hypersurfaces in Grassmannians,…

In this paper we consider the total space of the canonical bundle of P^2 and we use a proposal by Hosono, together with results in Seidel and Auroux-Katzarkov-Orlov, to deduce the right physical mirror equivalence between D^b(K_{P^2}) and…

Conformal self-dual fields in flat space-time of even dimension greater than or equal to four are studied. Ordinary-derivative formulation of such fields is developed. Gauge invariant Lagrangian with conventional kinetic terms and…

This paper gives an example of special Lagrangian manifold obtained from a hypersurface of a complex Grassmannian with vanishing first Chern class. The obtained manifold is a 1-torus bundle over the two dimensional real projective space.…

In [RW19] Rietsch and Williams relate cluster structures and mirror symmetry for type A Grassmannians Gr(k, n), and use this interaction to construct Newton-Okounkov bodies and associated toric degenerations. In this article we define a…

We construct a canonical frame for an arbitrary Gl(2)-structure thus solving the equivalence problem for Gl(2)-structures. Our treatment includes also a problem of contact equivalence of ordinary differential equations and applies to…

For all $m > 0$ we build a two-dimensional family of smooth manifolds of real dimension $3m + 2$ and use it to interpolate between the anticanonical family in the complex projective space of dimension $m + 1$ and its mirror dual. The main…

Let X be the toric variety (P^1)^4 associated with its four-dimensional polytope. Consider a resolution of the singular Fano variety associated with the dual polytope of X. Generically, anti-canonical sections Y of X and anticanonical…

Recent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects--the positive Grassmannian, positive loop Grassmannians, tree and loop Amplituhedra--which have been loosely…