A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Introduces new deformation classes in generalized Kähler geometry.
The paper connects Kähler-Ricci shrinkers to Fano fibrations in algebraic geometry.
Survey of recent metric geometry in Kähler metrics space.
The abstract discusses how generalized Calabi-Gray manifolds help solve non-Kähler geometry questions.
Unified Schwarz lemma in Kähler and Hermitian geometry.
The study of real Einstein submanifolds in Kähler geometry.
Quantizes geodesics in Kähler and Sasaki geometry.
Strong Kähler with Torsion is the target space geometry of and supersymmetric nonlinear sigma models. We discuss how it can be represented in terms of Generalised Complex Geometry in analogy to the Gualtieri map from the geometry of supersymmetric nonlinear sigma models to Generalised Kähler Geo…
We introduce and study the notion of a biholomorphic gerbe with connection. The biholomorphic gerbe provides a natural geometrical framework for generalized Kahler geometry in a manner analogous to the way a holomorphic line bundle is related to Kahler geometry. The relation between the gerbe and the generalized Kahler…
Paper solves open problem in complex Finsler geometry.
In the same way that a contact manifold determines and is determined by a symplectic cone, a Sasaki manifold determines and is determined by a suitable Kahler cone. Kahler-Sasaki geometry is the geometry of these cones. This paper presents a symplectic action-angle coordinates approach to toric Kahler geometry and how …
Study variational problems in Kähler geometry to construct metrics.
The abstract discusses how Kähler-Einstein metrics relate to algebraic geometry.
New submersions found in nearly Kähler geometry.
Study on GL(2) geometries on complex manifolds, focusing on Kähler-Einstein and Fano manifolds.
Survey on two non-Kähler geometry conjectures.
We review the information geometry of linear systems and its application to Bayesian inference, and the simplification available in the Kähler manifold case. We find conditions for the information geometry of linear systems to be Kähler, and the relation of the Kähler potential to information geometric quantities such …
Extends moment map concept to locally conformally Kähler manifolds.
This work is based on the talk delivered at Poisson 2008. We review the recent advances in Generalized Kahler geometry while stressing the use of Poisson and symplectic geometry. The derivation of the generalized Kahler potential is sketched and the relevant global issues are discussed.
Develops scalar curvature in generalized Kahler geometry and shows constant scalar curvature on compact Lie groups.
Survey on submanifolds in nearly Kähler spaces.
Surveying recent work on Kähler metrics and algebraic variety stability.
Generalized Kahler geometry is the natural analogue of Kahler geometry, in the context of generalized complex geometry. Just as we may require a complex structure to be compatible with a Riemannian metric in a way which gives rise to a symplectic form, we may require a generalized complex structure to be compatible wit…
We prove that any compact Kähler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact Kähler manifold.
Book introduces principles of LCK geometry for complex manifold students.
In this expository article we review the problem of finding Einstein metrics on compact Kähler manifolds and Sasaki manifolds. In the former half of this article we see that, in the Kähler case, the problem fits better with the notion of stability in Geometric Invariant Theory if we extend the problem to that of findin…
Study on non-Kähler Calabi-Yau geometries on 3-folds with constraints.
The goal of this note is to give an introduction to locally conformally symplectic and Kähler geometry. In particular, Sections 1 and 3 aim to provide the reader with enough mathematical background to appreciate this kind of geometry. The reference book for locally conformally Kähler geometry is "Locally conformal Kähl…
Uniform K-stability ensures existence of special metrics on toric manifolds.
Extends finite entropy measures in Kähler geometry.
We study the Kähler geometry of stage n Bott manifolds, which can be viewed as -dimensional generalizations of Hirzebruch surfaces. We show, using a simple induction argument and the generalized Calabi construction from [ACGT04,ACGT11], that any stage n Bott manifold admits an extremal Kähler metric. We also g…
We prove the correspondence between the information geometry of a signal filter and a Kähler manifold. The information geometry of a minimum-phase linear system with a finite complex cepstrum norm is a Kähler manifold. The square of the complex cepstrum norm of the signal filter corresponds to the Kähler potential. The…
We give an intrinsic definition of the special geometry which arises in global N=2 supersymmetry in four dimensions. The base of an algebraic integrable system exhibits this geometry, and with an integrality hypothesis any special Kahler manifold is so related to an integrable system. The cotangent bundle of a special …
We prove a general result about the geometry of holomorphic line bundles over Kahler manifolds.
We give a physical derivation of generalized Kahler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri regarding the equivalence between generalized Kahler geometry and the bi-hermitean geometry of Gates-Hull-Rocek. When cast in the language of supersymmetri…
Futaki invariant vanishes on Hopf manifolds.
In recent years, Streets and Tian introduced a series of curvature flows to study non-Kähler geometry. In this paper, we study how to construct second order curvature flows in a uniform way, under some natural assumptions which holds in Streets and Tian's works. As a result, by classifying the lower order tensors, we c…
Note removes degeneracy in Kähler geometry estimates.
Proves finite step termination of Kähler-Einstein metric singularity formation.
Study shows Kähler-Einstein metric singularities linked to curvature.
Surveying random sections on Kähler manifolds, leading to metrics.
The geometry of the target space of an N=(2,2) supersymmetry sigma-model carries a generalized Kahler structure. There always exists a real function, the generalized Kahler potential K, that encodes all the relevant local differential geometry data: the metric, the B-field, etc. Generically this data is given by nonlin…
Study Kähler geometry on vector bundles over elliptic curves.
Study shows continuity of non-Kähler Calabi-Yau conifold transitions.
It is known that the scalar curvature arises as the moment map in Kahler geometry. In pursuit of this analogy, we introduce the notion of a moment map in generalized Kahler geometry which gives the definition of a generalized scalar curvature on a generalized Kahler manifold. From the viewpoint of the moment map, we ob…
These notes, based on a graduate course I gave at Hamburg University in 2003, are intended to students having basic knowledges of differential geometry. Their main purpose is to provide a quick and accessible introduction to different aspects of Kähler geometry.
Study of complex 3-folds with vanishing Bismut Ricci form via special Kähler geometry.
Constructs hyper-Kähler models using Riemann-Hilbert problems.