6 papers
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 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…
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…
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…
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…