16 citations · 37 across the 19 of their papers we have counts for
20 papers
On the Localization of the Bergman Kernel and applications to Toeplitz theory
Siarhei Finski
For a compact complex manifold endowed with a big line bundle and a Radon measure, we study the localization phenomena of the associated Bergman (or Christoffel-Darboux) kernel. Fo…
Small eigenvalues of Toeplitz operators, Lebesgue envelopes and Mabuchi geometry
Siarhei Finski
We study small eigenvalues of Toeplitz operators on polarized complex projective manifolds. For Toeplitz operators whose symbols are supported on proper subsets, we prove the exist…
Toeplitz operators, submultiplicative filtrations and weighted Bergman kernels
Siarhei Finski
We demonstrate that the weight operator associated with a submultiplicative filtration on the section ring of a polarized complex projective manifold is a Toeplitz operator. We fur…
About Wess-Zumino-Witten equation and Harder-Narasimhan potentials
Siarhei Finski
For a polarized family of complex projective manifolds, we identify the algebraic obstructions that govern the existence of approximate solutions to the Wess-Zumino-Witten equation…
On Harder-Narasimhan slopes of direct images
Siarhei Finski
For a flat family of complex projective varieties, we study the asymptotic distribution of the Harder-Narasimhan slopes of the direct images on the base of high tensor powers of a…
Lower bounds on fibered Yang-Mills functionals: generic nefness and semistability of direct images
Siarhei Finski
The main goal of this paper is to generalize a part of the relationship between mean curvature and Harder-Narasimhan filtrations of holomorphic vector bundles to arbitrary polarize…
Geometry at the infinity of the space of positive metrics: test configurations, geodesic rays and chordal distances
Siarhei Finski
From the work of Phong and Sturm in 2007, for a polarised projective manifold and an ample test configuration, one can associate the geodesic ray of plurisubharmonic metrics on the…
Submultiplicative norms and filtrations on section rings
Siarhei Finski
We show that submultiplicative norms on section rings of polarised projective manifolds are asymptotically equivalent to sup-norms associated with metrics on the polarisation. We t…
On the metric structure of section ring
Siarhei Finski
The main goal of this article is to study for a projective manifold and an ample line bundle over it the relation between metric and algebraic structures on the associated section…
The asymptotics of the optimal holomorphic extensions of holomorphic jets along submanifolds
Siarhei Finski
We study the asymptotics of the -optimal holomorphic extensions of holomorphic jets associated with high tensor powers of a positive line bundle along submanifolds. More preci…
Complex embeddings, Toeplitz operators and transitivity of optimal holomorphic extensions
Siarhei Finski
In a setting of a complex manifold with a fixed positive line bundle and a submanifold, we consider the optimal Ohsawa-Takegoshi extension operator, sending a holomorphic section o…
Semiclassical Ohsawa-Takegoshi extension theorem and asymptotics of the orthogonal Bergman kernel
Siarhei Finski
We study the asymptotics of Ohsawa-Takegoshi extension operator and orthogonal Bergman projector associated with high tensor powers of a positive line bundle. More precisely, for a…
On Monge-Ampère volumes of direct images
Siarhei Finski
This paper is devoted to the study of the asymptotics of Monge-Ampère volumes of direct images associated with high tensor powers of an ample line bundle. We study the leading term…
On characteristic forms of positive vector bundles, mixed discriminants and pushforward identities
Siarhei Finski
We prove that Schur polynomials in Chern forms of Nakano and dual Nakano positive vector bundles are positive as differential forms. Moreover, modulo a statement about the positivi…
Spanning trees, cycle-rooted spanning forests on discretizations of flat surfaces and analytic torsion
Siarhei Finski
We study the asymptotic expansion of the determinant of the graph Laplacian associated to discretizations of a half-translation surface endowed with a flat unitary vector bundle. B…
Finite difference method on flat surfaces with a flat unitary vector bundle
Siarhei Finski
We establish an asymptotic relation between the spectrum of the discrete Laplacian associated to discretizations of a half-translation surface with a flat unitary vector bundle and…
Quillen metric for singular families of Riemann surfaces with cusps and compact perturbation theorem
Siarhei Finski
We study the behavior of the Quillen metric for the family of Riemann surfaces with cusps when the additional cusps are created by degeneration. More precisely, in our previous pap…
Analytic torsion for surfaces with cusps II. Regularity, asymptotics and curvature theorem
Siarhei Finski
In this article we study the Quillen norm on the determinant line bundle associated with a family of complex curves with cusps, which admit singular fibers. More precisely, we fix…
Analytic torsion for surfaces with cusps I. Compact perturbation theorem and anomaly formula
Siarhei Finski
Let be a compact Riemann surface and let be a metric over , where is a finite set of points. We suppo…
On the full asymptotic of analytic torsion
Siarhei Finski
The purpose of this article is to study the asymptotic expansion of Ray-Singer analytic tosion associated with increasing powers p of a given positive line bundle. Here we prove th…