Related papers: On the complement of a hypersurface with flat norm…
We introduce a symplectic structure on the space of connections in a G-principal bundle over a four-manifold and the Hamiltonian action on it of the group of gauge transformations which are trivial on the boundary. The symplectic reduction…
In the present article we work out a relative setup of generic structures on surface singularities. We fix an analytic type on a subgraph of a rational homology sphere resolution graph $\mathcal{T}$ and we choose a relatively generic normal…
We introduce a class of semipositive metrics on ample line bundles in non-Archimedean geometry, called Shilov finite metrics. We calculate the determinant metric distorsion in the exact sequence induced by a global section using…
Quantum systems are often classified into Hermitian and non-Hermitian ones. Extraordinary non-Hermitian phenomena, ranging from the non-Hermitian skin effect to the supersensitivity to boundary conditions, have been widely explored. Whereas…
Our recent work about fully non-linear elliptic equations on compact manifolds with a flat hyperk\"ahler metric is hereby extended to the parabolic setting. This approach will help us to study some problems arising from hyperhermitian…
The density of the hyperbolic metric on the complement of a rectangular lattice is investigated. The question is related to conformal mapping of symmetric circular quadrilaterals with all zero angles.
Let $X$ be a compact K\"ahler manifold and $\alpha$ be a class in the Dolbeault cohomology class of bidegree $(1, 1)$ on $X$. When the numerical dimension of $\alpha$ is one and $\alpha$ admits at least two smooth semi-positive…
In this review the foundations of Geometric Quantization are explained and discussed. In particular, we want to clarify the mathematical aspects related to the geometrical structures involved in this theory: complex line bundles, hermitian…
Generalizing the recent result of Berndtsson, we prove the Nakano semipositivity of the direct image of relative pluricanonical systems and the direct image of relative adjoint (singular) hermitian line bundle with semipositive curvature.…
The self-duality equations on a Riemann surface arise as dimensional reduction of self-dual Yang-Mills equations. Hitchin had showed that the moduli space ${\mathcal M}$ of solutions of the self-duality equations on a compact Riemann…
We introduce the concept of a Fock bundle, a smooth principal bundle over a surface equipped with a special kind of adjoint-valued 1-form, as a new tool for studying character varieties of surface groups. Although similar to Higgs bundles,…
Using techniques of supersymmetric gauge theories, we present the Ricci-flat metrics on non-compact Kahler manifolds whose conical singularity is repaired by the Hermitian symmetric space. These manifolds can be identified as the complex…
In this paper, we investigate the existence of weak singular Hermite-Einstein structures on homogeneous holomorphic vector bundles over rational homogeneous varieties. Using Cartan's highest weight theory, we establish an explicit algebraic…
The authors study the geometry of lightlike hypersurfaces on manifolds $(M, c)$ endowed with a pseudoconformal structure $c = CO (n - 1, 1)$ of Lorentzian signature. Such hypersurfaces are of interest in general relativity since they can be…
We study singular Hermitian metrics on vector bundles. There are two main results in this paper. The first one is on the coherence of the higher rank analogue of multiplier ideals for singular Hermitian metrics defined by global sections.…
We study the asymptotic behavior of Hitchin's hyperk\"ahler metric on the moduli space of rank two irregular Higgs bundles over $\mathbb{C}P^1$. Along a generic curve, we prove that the Hitchin metric is asymptotic to the semiflat metric at…
In this paper, we prove a total curvature estimate of closed hypersurfaces in simply-connected non-positively curved symmetric spaces, and as a corollary, we obtain an isoperimetric inequality for such manifolds.
We calculate curvature tensors of metrics on the total spaces of holomorphic fibrations. Our main tool is a theory of Chern connections and curvature forms for possibly degenerate Hermitian forms on holomorphic vector bundles. We prove a…
Deng-Ning-Wang-Zhou showed that a Hermitian holomorphic vector bundle is Griffiths semi-positive if it satisfies the optimal $L^2$-extension condition. As a generalization, we present a quantitative characterization of Griffiths positivity…
We prove that for any germ of complex analytic set in $\CC^n$ there exists a hypersurface singularity whose Milnor fibration has trivial geometric monodromy and fibre homotopic to the complement of the germ of complex analytic set. As an…