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Mihai Paun

Publications and source records attributed to Mihai Paun.

At least 19 recordsLinked to original sources
arXiv2026

Two-step nilpotent monodromy of local systems on special varieties

Let $X$ be a smooth complex quasi-projective variety that is special in the sense of Campana. We prove that the monodromy group of any complex local system on $X$ is virtually nilpotent of class at most $2$. This result sharply refines a theorem of Cadorel, Yamanoi, and the second author. To establish this result, we develop a deformation theory for certain local systems on quasi-compact K\"ahler manifolds by constructing universal deformations for such local systems. As a byproduct of our argument, we also show that a general fiber of the quasi-Albanese map of $X$ is special, extending a result of Campana and Claudon from the projective to the quasi-projective setting.

math.AG↗
arXiv2025

Hodge theory for local systems and cohomological support loci

In this article, we pursue two main objectives. The first is to show that the fundamental results of Green-Lazarsfeld (1987, 1991) on generic vanishing theorems, and works of Budur-Wang (2015, 2020) on cohomology jumping loci, can be established within a unified framework based on suitable versions of the $\partial\bar{\partial}$-lemma. Our second-and primary-goal is to develop the technical tools required for this approach, namely an $L^2$-Hodge theory for the cohomology of rank-one local systems on quasi-compact K\"ahler manifolds. Further developments concerning higher-rank local systems, as well as several geometric applications, will be presented in a companion paper and are briefly outlined in the introduction.

math.AG↗
arXiv2024

On the Canonical Bundle Formula and Adjunction for Generalized Kaehler Pairs

In this article we prove analogs of Kawamata's canonical bundle formula, Kawamata subadjunction and plt/lc inversion of adjunction for generalized pairs on Kaehler varieties. We also show that a conjecture of BDPPin dimension n-1 implies that the cone theorem holds for any n-dimensional Kaehler generalized klt pair. Along the way, we obtain more complete versions of some results due to Collins-Tosatti and Cao-Hoering.

math.AG↗
arXiv2024

Hermite--Einstein metrics in singular settings

In this article we pursue the following main goals. In the first place, we establish the existence of "estimable" Hermite--Einstein metrics for stable reflexive coherent sheaves on compact normal Kähler spaces. If moreover the background variety has klt singularities, we obtain a much more precise result.

math.DG↗
arXiv2023

Infinitesimal extension of pluricanonical forms

The current paper represents the first part: it contains the results concerning the lifting of twisted canonical sections defined on an infinitesimal neighborhood of the central fiber of a smooth, proper Kähler family which verify a natural L2 condition.

math.AG↗
arXiv2020

On the Ohsawa-Takegoshi extension theorem

We establish a new extension result for twisted canonical forms defined on a hypersurface with simple normal crossings of a projective manifold. Some of the examples presented in the appendix are showing that the bounds we obtain for the extension are sharp.

math.CV↗
arXiv2019

Algebraic fiber spaces and curvature of higher direct images

In this article we are interested in the differential geometric properties of certain higher direct images of exterior powers of the sheaf of relative differentials twisted with a line bundle. We obtain explicit curvature formulas, especially in case where the said line bundle satisfies a natural curvature assumption. Several applications are obtained, including a proof of a result by Viehweg-Zuo in the context of a canonically polarized family of maximal variation.

math.DG↗
arXiv2017

Value Distribution Theory for Parabolic Riemann Surfaces

We survey several results in value distribution theory for parabolic Riemann surfaces. Let Y be a parabolic Riemann surface, i.e. subharmonic functions defined on Y are constant. We discuss Nevanlinna's theory for holomorphic maps f from Y to the projective line. The results we obtain parallel the classical case Y is the complex line, as we describe now. Let X be a manifold of general type, and let A be an ample line bundle on X. It is known that there exists a holomorphic jet differential P (of order k) with values in the dual of A. If the map f has infinite area and if Y has finite Euler characteristic, then we show that f satisfies the differential relation induced by P. As a consequence, we obtain a generalization of Bloch Theorem concerning the Zariski closure of maps f with values in a complex torus. An interesting corollary of these techniques is a refined Ax-Lindemann theorem, for which we give a quick proof. We then study the degree of Nevanlinna's current T[f] associated to a parabolic leaf of a foliation F by Riemann surfaces on a compact complex manifold. We show that the degree of T[f] on the tangent bundle of the foliation is bounded from below in terms of the counting function of f with respect to the singularities of F, and the Euler characteristic of Y. In the case of complex surfaces of general type, we obtain a complete analogue of McQuillan's result: a parabolic curve of infinite area and finite Euler characteristic tangent to F is not Zariski dense.

math.CV↗
arXiv2017

Foliations with positive slopes and birational stability of orbifold cotangent bundles

In this article we consider log canonical pairs which are log-smooth. If the corresponding canonical bundle is pseudo-effective, then we show that any quotient of the orbifold cotangent bundle of the pair has a pseudo-effective determinant. One of the new ingredients in the proof is a generalization of the Bogomolov-McQuillan algebraicity criterion in the context of holomorphic foliations whose minimal slope with respect to a movable class is positive.

math.AG↗
arXiv2016

Orbifold Slope Rational-Connectedness

The notion of 'slope rational connectedness' is introduced in the context of smooth orbifold pairs. The main result parallels the characterization of the rational connectedness of projective manifolds in terms of either the non-existence of holomorphic covariant tensors, or of absence of fibrations onto manifolds with pseudo-effective canonical bundle, or of existence of movable classes for which the minimal slope of the tangent bundle is positive. We then use this result to construct the `rational quotient map' in orbifold category.

math.AG↗
arXiv2012

Relative adjoint transcendental classes and Albanese maps of compact Kaehler manifolds with nef Ricci curvature

Given a surjective holomorphic map between two compact Kaehler manifolds, we investigate the positivity properties of relative adjoint transcendental classes which are inherited from similar fiberwise properties. As a consequence, we solve a problem proposed by J.-P. Demailly, T. Peternell and M. Schneider concerning the Albanese morphism of Kaehler manifolds with nef anticanonical class.

math.CV↗