arXiv research

Study hyperbolic 2-spheres with cone points, describing spaces for n=3.

Study on curves on specific arithmetic quotients of hyperbolic 2-ball.

New 2D complex hyperbolic structures found on sphere orbibundles.

The Siu-Yang conjecture is reviewed for complex 2-manifolds.

We describe and study the loci equidistant from finitely many points in the so-called complex hyperbolic geometry, i.e., in the geometry of a holomorphic $2$-ball $\Bbb B$. In particular, we show that the bisectors (= the loci equidistant from $2$ points) containing the (smooth real algebraic) curve equidistant from gi…

Holomorphic curves found in compact quotients of SL(2,C).

We prove an equidistribution result for totally geodesic submanifolds in a compact locally symmetric space. In the case of Hermitian locally symmetric spaces, this gives a convergence theorem for currents of integration along totally geodesic subvarieties. As a corollary, we obtain that on a complex surface which is a …

Holomorphic curves found in compact quotients of SL(2,C).

In this article we prove first of all the nonexistence of holomorphic submersions other than covering maps between compact quotients of complex unit balls, with a proof that works equally well in a more general equivariant setting. For a non-equidimensional surjective holomorphic map between compact ball quotients, our…

In the current article our primary objects of study are compact complex submanifolds of quotient manifolds of irreducible bounded symmetric domains by torsion free discrete lattices of automorphisms. We are interested in the characterization of the totally geodesic submanifolds among compact splitting complex submanifo…

Symplectic reduction extended to Sasakian manifolds.

In this paper we study numerical properties of quotients of holomorphic log-tensors.

A new method shows open Riemann surfaces have finite genus.

This paper provides an explicit form for symmetric differentials and their corresponding holomorphic functions.

The paper proves a structure theorem for compact Kähler manifolds with semi-positive holomorphic sectional curvature.

Decomposes complex manifolds with trivial canonical bundle into homogeneous structures.

Study of complex projective manifolds using arithmetic lattices.

We introduce Morse-type inequalities for a holomorphic circle action on a holomorphic vector bundle over a compact Kaehler manifold. Our inequalities produce bounds on the multiplicities of weights occurring in the twisted Dolbeault cohomology in terms of the data of the fixed points and of the symplectic reduction. Th…

The paper studies spaces of non-compact real algebraic curves and their uniformisation.

Constructs a moment map for maps to balanced manifolds.

Let M be a complex nilmanifold, that is, a compact quotient of a nilpotent Lie group endowed with an invariant complex structure by a discrete lattice. A holomorphic differential on M is a closed, holomorphic 1-form. We show that $a(M)\leq k$, where $a(M)$ is the algebraic dimension $a(M)$ (i.e. the transcendence degre…

Embeds CR manifolds into complex spaces using equivariant actions.

The note confirms a conjecture for specific Lie groups.

Study geodesics on ball quotients to find nonvanishing sections.

Study numerically flat bundles on Fujiki manifolds using algebraic groups.

Kähler submanifolds in Iwasawa manifolds are studied.

Let $X$ be a compact connected Riemann surface of genus $g$, with $g \geq 2$, and let ${\mathcal O}_X$ denote the sheaf of holomorphic functions on $X$. Fix positive integers $r$ and $d$ and let ${\mathcal Q}(r,d)$ be the Quot scheme parametrizing all torsion coherent quotients of ${\mathcal O}^{\oplus r}_X$ of degree …

Study numerically flat bundles on non-Kähler manifolds.

We define geometric zeta functions for locally symmetric spaces as generalizations of the zeta functions of Ruelle and Selberg. As a special value at zero we obtain the Reidemeister torsion of the manifold. For hermitian spaces these zeta functions have as special value the quotient of the holomorphic torsion of Ray an…

The paper confirms conjectures about Stein manifolds formed by quotients of the ball.

Kirwan surjectivity proven for equivariant Dolbeault cohomology.

Study gauge theory of real and quaternionic parabolic bundles over real curves.

SU(n)-structures derived from Kähler manifolds with torus actions.

In this article we study compact Kähler manifolds $X$ admitting non-singular holomorphic vector fields with the aim of extending to this setting the classical birational classification of projective varieties with tangent vector fields. We prove that any such a Kähler manifold $X$ admits an arbitrarily small deformatio…

Defines character varieties for real forms of complex classical groups and proves their properties.

Study compares Kähler quotients of torus actions under varying moment maps.

We investigate representations of Kähler groups $Γ= π_1(X)$ to a semisimple non-compact Hermitian Lie group $G$ that are deformable to a representation admitting an (anti)-holomorphic equivariant map. Such representations obey a Milnor--Wood inequality similar to those found by Burger--Iozzi and Koziarz--Maubon. Thanks…

An LCK manifold with potential is a compact quotient M of a Kahler manifold X equipped with a positive plurisubharmonic function f, such that the monodromy group acts on $X$ by holomorphic homotheties and maps f to a function proportional to f. It is known that M admits an LCK potential if and only if it can be holomor…

Let $S^n(X)$ be the $n$-fold symmetric product of a compact connected Riemann surface $X$ of genus $g$ and gonality $d$. We prove that $S^n(X)$ admits a Kähler structure such that all the holomorphic bisectional curvatures are nonpositive if and only if $n < d$. Let ${\mathcal Q}_X(r,n)$ be the Quot scheme parametrizin…

The study solves open problems in complex geometry by analyzing bounded domains with finite-volume quotients.

Paper proves Chern flat for 3D Hermitian manifolds with zero real bisectional curvature.

Classifies 6D homogeneous spaces with holomorphically trivial canonical bundle.

Holomorphic bundles on complex manifolds with boundary are studied, extending results from Donaldson's work.

New method constructs non-arithmetic hyperbolic orbifolds from complex arithmetic ball quotients.

Geometric Invariant Theory applied to Kähler manifolds yields analytic models for vector bundles.

Prove long-time existence of pluriclosed flow on certain fibrations

Holomorphic tensors on Vaisman manifolds are invariant under the Lee field.

No exact G₂-structures on compact Lie group quotients.