Related papers: Spectra and strains

This paper generalizes the first author's preceding works concerning admissible functions on certain Fano manifolds. Here, we study a larger class of functions which can be less symmetric than the ones studied before. When the sup of these…

In 1991 Campana and Peternell proposed, as a natural algebro-geometric extension of Mori's characterization of the projective space, the problem of classifying the complex projective Fano manifolds whose tangent bundle is nef, conjecturing…

Let X be a connected family of complex Fano manifolds. We show that if some fiber is the product of two manifolds of lower dimensions, then so is every fiber. Combining with previous work of Hwang and Mok, this implies immediately that if a…

We give the site-theoretic account of the spectral construction as first introduced by Coste. We provide a detailed examination of the geometric properties of the spectrum, in particular what classes of topoi it produces when applied to the…

The theory of graphons has proven to be a powerful tool in many areas of graph theory. In this paper, we introduce several foundational aspects of the theory of digraphons -- asymmetric two-variable functions that arise as limits of…

We derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary length. The implications of our results to the structural and dynamical properties of networks…

In this expository article we first give an overview on multiplier ideal sheaves and geometric problems in K\"ahlerian and Sasakian geometries. Then we review our recent results on the relationship between the support of the subschemes cut…

In this note, we prove two results regarding the variation of K-moduli. The first one reveals the relationship between the chamber decomposition for K-semistable domains and the variation of GIT. The second one presents the relationship…

The quantum period of a variety X is a generating function for certain Gromov-Witten invariants of X which plays an important role in mirror symmetry. In this paper we compute the quantum periods of all 3-dimensional Fano manifolds. In…

The spectral problem on a periodic domain with cracks is studied. An asymptotic form of dispersion relations is calculated under assumption that the opening of the cracks is small.

In the present paper we discuss coherent sheaves of rank > 1 whose projectivization gives rise to smooth varieties - varieties of this type are also called smooth scrolls. We prove some basic properties of these varieties and we give some…

We study the arithmetic of division fields of semistable abelian varieties A over the rationals. The Galois group of the 2-division field of A is analyzed when the conductor is odd and squarefree. The irreducible semistable mod 2…

We describe local mirror symmetry from a mathematical point of view and make several A-model calculations using the mirror principle (localization). Our results agree with B-model computations from solutions of Picard-Fuchs differential…

We study rational curves on general Fano hypersurfaces in projective space, mostly by degenerating the hypersurface along with its ambient projective space to reducible varieties. We prove results on existence of low-degree rational curves…

We define vector fields, leaves and trajectories for schemes. With these tools, we are able to give a geometrical interpretation and to generalize several results of differential Galois theory and constructions on differential schemes. We…

We propose localization techniques for computing Gromov-Witten invariants of maps from Riemann surfaces with boundaries into a Calabi-Yau, with the boundaries mapped to a Lagrangian submanifold. The computations can be expressed in terms of…

Given any field $k$ (not necessarily perfect), we study the smoothing of a semistable Fano variety over $k$. In characteristic 0, the reduced semistable Fano degenerate fibers of Mori fibrations are classified. In positive characteristic,…

We describe spectra of associative (not necessarily unital and not necessarily countable-dimensional) locally matrix algebras. We determine all possible spectra of locally matrix algebras and give a new proof of Dixmier-Baranov Theorem. As…

We prove that open Gromov-Witten invariants for semi-Fano toric manifolds of the form $X=\mathbb{P}(K_Y\oplus\mathcal{O}_Y)$, where $Y$ is a toric Fano manifold, are equal to certain 1-pointed closed Gromov-Witten invariants of $X$. As…

Some questions of application of trigonometric splines in problems of spectral analysis are considered. The known effects of overlay in the frequency and time domains are discussed; deployment effects in these areas are firstly considered.…