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.
Cubic fourfolds have K-stability and admit Kähler-Einstein metrics.
We prove that various GIT semistabilities of polarized varieties imply semi-log-canonicity.
In this note, we shall show that the Chow-stability and the Hilbert-stability in GIT asymptotically coincide.
Study homotopy groups in GIT quotients using transversality methods.
Surveying progress on deformed Hermitian-Yang-Mills equation and its connections to stability.
The paper studies equivariant sheaves on toric varieties and their quotients.
We prove the K-moduli space of cubic threefolds is identical to their GIT moduli. More precisely, the K-(semi,poly)-stability of cubic threefolds coincide to the corresponding GIT stabilities, which could be explicitly calculated. In particular, this implies that all smooth cubic threefolds admit Kähler-Einstein metric…
Introduces stability for families of K-polystable varieties and connects it to optimal symplectic connections.
New criterion for solving inverse Hessian equations, including J-equation.
We give a complete criterion for the existence of generalized Kähler Einstein metrics on toric Fano manifolds from view points of a uniform stability in a sense of GIT and the properness of a functional on the space of Kähler metrics.
This survey intends to present the basic notions of Geometric Invariant Theory (GIT) through its paradigmatic application in the construction of the moduli space of holomorphic vector bundles. Special attention is paid to the notion of stability from different points of view and to the concept of maximal unstability, r…
We study the deformed Hermitian-Yang-Mills (dHYM) equation, which is mirror to the special Lagrangian equation, from the variational point of view via an infinite dimensional GIT problem mirror to Thomas' GIT picture for special Lagrangians. This gives rise to infinite dimensional manifold mirror to Solom…
Study links K-stability of certain surfaces to binary forms, proving stability and non-stability conditions.
We provide examples of families of (log) smooth canonically polarized varieties, including smooth weighted pointed curves and smooth hypersurfaces in with large degree such that the Chow semistable limits under distinct pluricanonical embeddings do not stabilize.
New examples of Kähler-Ricci solitons on Fano threefolds with non-trivial moduli found.
G. Tian and S.K. Donaldson formulated a conjecture relating GIT stability of a polarized algebraic variety to the existence of a Kahler metric of constant scalar curvature. In [Don02] Donaldson partially confirmed it in the case of projective toric varieties. In this paper we extend Donaldson's results and computations…
An introduction is provided to some current research trends in stability in geometric invariant theory and the problem of Kaehler metrics of constant scalar curvature. Besides classical notions such as Chow-Mumford stability, the emphasis is on several new stability conditions, such as K-stability, Donaldson's infinite…
Solves existence of gravitating vortices with positive curvature.
For a polarized Kähler manifold , we show the equivalence between relative balanced embeddings introduced by Mabuchi and -balanced embeddings introduced by Sano, answering a question of Hashimoto. We give a GIT characterization of the existence of a -balanced embedding, and relate the optimal weight t…
GIT-Net uses neural networks to approximate PDE operators efficiently.
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…
It is conjectured that the existence of constant scalar curvature Kähler metrics will be equivalent to K-stability, or K-polystability depending on terminology (Yau-Tian-Donaldson conjecture). There is another GIT stability condition, called the asymptotic Chow polystability. This condition implies the existence of bal…
We introduce a notion of stability for sheaves with respect to several polarisations that generalises the usual notion of Gieseker-stability. We prove, under a boundedness assumption, which we show to hold on threefolds or for rank two sheaves on base manifolds of arbitrary dimension, that semistable sheaves have a pro…
Study real forms and GIT quotients in algebraic varieties.
In this paper we study the relative Chow and -stability of toric manifolds in the toric sense. First, we give a criterion for relative -stability and instability of toric Fano manifolds in the toric sense. The reduction of relative Chow stability on toric manifolds will be investigated using the Hibert-Mumford cr…
We embed polarised orbifolds with cyclic stabiliser groups into weighted projective space via a weighted form of Kodaira embedding. Dividing by the (non-reductive) automorphisms of weighted projective space then formally gives a moduli space of orbifolds. We show how to express this as a reductive quotient and so a GIT…
Study shows K-moduli spaces connect quartic surfaces to K3 surfaces, verifying predictions and classifying degenerations.
Abstract: Generalizes stability theories over toric varieties and Novikov type rings.
Quantum Kirwan maps between K-theories of G-varieties and GIT quotients.
There is an obstruction to the existence of Kähler -Einstein metrics which is used to define the GIT weight for K-stability, and it has been extended to various geometric problems. This survey paper considers such extended obstructions to the existence problem of Kähler -Ricci solitons, Sasaki-Einstein metrics and (con…
In this paper, we prove that any two birational projective varieties with finite quotient singularities can be realized as two geometric GIT quotients of a non-singular projective variety by a reductive algebraic group. Then, by applying the theory of Variation of Geometric Invariant Theory Quotients ([3]), we show tha…
New polystability theory connects Calabi-Yau varieties to gravitational instantons.
GIT uses gradient estimators to target interventions for causal discovery.
Study describes signatures of Ricci curvature on nilmanifolds.
Paper presents a new method for pricing American options with hybrid dividends.
Defines kappa classes on KSBA spaces, generalizing classes on curves.
The paper proves a theorem about constructing Higgs bundle moduli space.
Motivated by Wick-rotations of pseudo-Riemannian manifolds, we study real geometric invariant theory (GIT) and compatible representations. We extend some of the results from earlier works \cite{W2,W1}, in particular, we give some sufficient as well as necessary conditions for when pseudo-Riemannian manifolds are Wick-r…
The moduli space of smooth real binary octics has five connected components. They parametrize the real binary octics whose defining equations have 0, 1, ..., 4 complex-conjugate pairs of roots respectively. We show that the GIT-stable completion of each of these five components admits the structure of an arithmetic rea…
We define Wick-rotations by considering pseudo-Riemannian manifolds as real slices of a holomorphic Riemannian manifold. From a frame bundle viewpoint Wick-rotations between different pseudo-Riemannian spaces can then be studied through their structure groups which are real forms of the corresponding complexified Lie g…
The 'moduli continuity method' permits an explicit algebraisation of the Gromov-Hausdorff compactification of Kähler-Einstein metrics on Fano manifolds in some fundamental examples. In this paper, we apply such method in the 'log setting' to describe explicitly some compact moduli spaces of K-polystable log Fano pairs.…
Develops a new method for pricing barrier options in time-dependent Heston model.
Extends probabilistic approach for Kahler-Einstein metrics on Fano manifolds.
In this paper, we propose a weak version of quotient for the algebraic action of a group on a variety, which we shall call a pseudo-quotient. They arise when we focus on the purely topological properties of good GIT quotients regardless of their algebraic properties. The flexibility granted by their topological nature …
Extending work of Bielawski-Dancer and Konno, we develop a theory of toric hyperkahler varieties, which involves toric geometry, matroid theory and convex polyhedra. The framework is a detailed study of semi-projective toric varieties, meaning GIT quotients of affine spaces by torus actions, and specifically, of Lawren…
Geometric Invariant Theory applied to Kähler manifolds yields analytic models for vector bundles.
Integrates fairness guarantees into deep learning models.
We show that homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds, using that they admit periodic, integrally minimal foliations by homogeneous hypersurfaces. For the geometric flow induced by the orbit-Einstein condition, we construct a Lyapunov function based on curvature estimates which come f…