Related papers: On the Chern numbers of a smooth threefold
We survey various quantized bulk physical observables in two- and three-dimensional topological band insulators invariant under translational symmetry and crystallographic point group symmetries (PGS). In two-dimensional insulators, we show…
We obtain several new characterizations of splayedness for divisors: a Leibniz property for ideals of singularity subschemes, the vanishing of a `splayedness' module, and the requirements that certain natural morphisms of modules and…
Local topological markers are used to characterize Chern insulators in the presence of spatial inhomogeneities, such as boundaries and disorder. In this paper, we study the local Chern marker in systems with partial translational symmetry.…
In 2D semiconductors and insulators, the Chern number of the valence band Bloch state is an important quantity that has been linked to various material properties, such as the topological order. We elaborate that the opacity of 2D materials…
This paper extends a number of known results on slope-semistable sheaves from the classical case to the setting where polarisations are given by movable curve classes. As applications, we obtain new flatness results for reflexive sheaves on…
The use of topological invariants to describe geometric phases of quantum matter has become an essential tool in modern solid state physics. The first instance of this paradigmatic trend can be traced to the study of the quantum Hall…
We first construct closed spherical CR manifolds of dimension at least five having non-trivial first Chern class with real coefficients. We next prove a constraint on Chern classes with real coefficients of (not necessarily closed)…
A central property of Chern insulators is the robustness of the topological phase and edge states to impurities in the system. Despite this, Chern number cannot be straightforwardly calculated in the presence of disorder. Recently, work has…
Recently, Chern vector with arbitrary formula $\textbf{C}\!=\!(\mathcal{C}_{yz},\mathcal{C}_{xz},\mathcal{C}_{xy})$ in three-dimensional systems has been experimentally realized [\B{Nature 609, 925 (2022)}]. Motivated by these progresses,…
We prove existence of reflexive sheaves on singular surfaces and threefolds with prescribed numerical invariants and study their moduli.
A classification and a detailed geometric description are given for smooth $n$-dimensional subvarieties $X\subset{\mathbb P}^{2n-1}$ containing a family of effective divisors each of them spanning a linear ${\mathbb P}^n$ of ${\mathbb…
The aim of this note is to improve upon our earlier result which translates Weyl's (curvature) formulation of Chern character of a smooth vector bundle into the language of residues. The dualized Chern character is the functional on smooth…
We investigate Gromov-Witten invariants associated to exceptional classes for primitive birational contractions on a Calabi-Yau threefold X. It was observed in a previous paper that these invariants are locally defined, in that they can be…
We study motivic Chern classes of cones. First we show examples of projective cones of smooth curves such that their various $K$-classes (sheaf theoretic, push-forward and motivic) are all different. Then we show connections between the…
We study the relation between Chern numbers and Quantum Phase Transitions (QPT) in the XY spin-chain model. By coupling the spin chain to a single spin, it is possible to study topological invariants associated to the coupling Hamiltonian.…
In this note, we extend the theory of Chern-Cheeger-Simons to construct canonical invariants for a one-parameter family of flat connections on a smooth manifold. These invariants lie in degrees $(2p-2)$-cohomology with $\C/\Z$-cohomology,…
Chern-Simons invariants of closed oriented Riemannian $3$-manifolds are introduced and studied from the basics. Their first-order variation is the Cotton tensor. The properties of the Cotton tensor: symmetry, conformal covariance, trace-…
Topological phases have greatly improved our understanding of modern conception of phases of matter that go beyond the paradigm of symmetry breaking and are not described by local order parameters. Instead, characterization of topological…
Divisorial contractions to singularities, defined by equations $xy+z^n+u^n=0$ $n\ge3$ and $xy+z^3+u^4=0$ are classified.
% A new, formal, non-combinatorial approach to invariants of % three-dimensional manifolds of Reshetikhin, Turaev and % Witten in the framework of non-perturbative topological % quantum Chern-Simons theory, corresponding to an arbitrary %…