arXiv research

New derivation of Type IIA flow metrics.

The paper proves heat kernel asymptotics for high power line bundles on complex manifolds.

Let $(X,h)$ be a compact and irreducible Hermitian complex space of complex dimension $v>1$. In this paper we show that the Friedrichs extension of both the Laplace-Beltrami operator and the Hodge-Kodaira Laplacian acting on functions has discrete spectrum. Moreover we provide some estimates for the growth of the corre…

The paper studies spectral convergence of Hodge-Kodaira Laplacians on degenerating Hermitian metrics.

Paper solves a metric-independent problem on almost Kähler 4-manifolds.

The paper extends Bott-Chern Laplacian definition and explores its properties on almost Hermitian manifolds.

Study estimates the first eigenvalue on Kähler manifolds with specific curvature conditions.

Eigenvalue estimates for Hodge Laplacian on Fano manifolds lead to geometric insights.

Study on Kähler manifolds proves weak decompositions and relates harmonic forms.

The paper improves $L^2$-estimates for Dirac-Dolbeault operators on complex manifolds.

The paper provides estimates for higher-order Ricci curvature along Kähler-Ricci flows.

Study on $4$-dimensional almost-Hermitian manifolds, proving $\overline\partial$-harmonic forms invariant under certain metrics.

We study two quantization schemes for compact symplectic manifolds with almost complex structures. The first of these is the Spin-c quantization. We prove the analog of Kodaira vanishing for the Spin-c Dirac operator, which shows that the index space of this operator provides an honest (not virtual) vector space semicl…

Defines and classifies Thurston geometries and connects simplicial volume to Kodaira dimension.

Let $X$ be an abstract not necessarily compact orientable CR manifold of dimension $2n-1$, $n\geqslant2$, and let $L^k$ be the $k$-th tensor power of a CR complex line bundle $L$ over $X$. Given $q\in\set{0,1,\ldots,n-1}$, let $\Box^{(q)}_{b,k}$ be the Gaffney extension of Kohn Laplacian for $(0,q)$ forms with values i…

Extends Kodaira Spencer to higher-dimensional Calabi-Yau manifolds.

Let $(X,h)$ be a compact and irreducible Hermitian complex space of complex dimension $m$. In this paper we are interested in the Dolbeault operator acting on the space of $L^2$ sections of the canonical bundle of $reg(X)$, the regular part of $X$. More precisely let $\overline{\mathfrak{d}}_{m,0}:L^2Ω^{m,0}(reg(X),h)\…

Proves Vaisman solvmanifolds are finite quotients of Kodaira-Thurston manifolds.

Study on Kodaira dimension of SU(m)-structures on almost complex manifolds.

Study Kodaira dimensions on almost complex manifolds, proving integrability and structural descriptions.

Automorphisms of Kodaira surfaces are shown to be affine transformations.

Computational techniques calculate dimensions of complex structures.

In this note we show that the Lagrangian Luttinger surgery preserves the symplectic Kodaira dimension. Some constraints on Lagrangian tori in symplectic four manifolds with non-positive Kodaira dimension are also derived.

Study extra-special quotients of surface braid groups and construct double Kodaira fibrations.

Study on Vaisman metrics on Kodaira-Thurston surface using pluriclosed flow.

We bound the index of a subgroup in iterated Kodaira fibrations.

New findings on Frobenius structures on Kodaira manifolds.

Generalizes Kodaira vanishing theorem to Kahler Lie algebroids.

We define the Kodaira dimension for $3$-dimensional manifolds through Thurston's eight geometries, along with a classification in terms of this Kodaira dimension. We show this is compatible with other existing Kodaira dimensions and the partial order defined by non-zero degree maps. For higher dimensions, we explore th…

The notion of Kodaira dimension has recently been extended to general almost complex manifolds. In this paper we focus on the Kodaira dimension of almost Kähler manifolds, providing an explicit computation for a family of almost Kähler threefolds on the differentiable manifold underlying a Nakamura manifold. We concent…

The paper explores Kodaira dimension on almost complex manifolds.

The paper uses non-abelian Hodge theory to generalize Kodaira vanishing theorems.

Method solves $\bar\partial$-harmonic forms on Kodaira-Thurston manifold.

We define analogue of theta-functions on the Kodaira--Thurston manifold which is a compact 4-dimensional symplectic manifold and use them to construct canonical symplectic embedding of the Kodaira--Thurston manifold into the complex projective space (analogue of the Lefshetz theorem).

We provide infinitely many examples of pairs of diffeomorphic, non simply connected K\" ahler manifolds of complex dimension three with different Kodaira dimensions. Also, in any possible Kodaira dimension we find infinitely many pairs of non deformation equivalent, diffeomorphic K\" ahler threefolds.

The paper examines Kodaira dimensions of specific complex 4-manifolds with torsion first Chern class.

We consider a general Hermitian holomorphic line bundle $L$ on a compact complex manifold $M$ and let ${\Box}^q_p$ be the Kodaira Laplacian on $(0,q)$ forms with values in $L^p$. The main result is a complete asymptotic expansion for the semi-classically scaled heat kernel $\exp(-u{\Box}^q_p/p)(x,x)$ along the diagonal…

Study on Kodaira dimension of specific solvmanifolds without complex structures.

Abstract: Almost Kähler Hodge numbers vary with metric choices.

Given a smooth positive measure $μ$ on a complete Hermitian manifold with Ricci curvature bounded from below, we prove a pointwise Agmon-type bound for the corresponding Bergman kernel, under rather general conditions involving the coercivity of an associated complex Laplacian on $(0,1)$-forms. Thanks to an appropriate…

Analyzes Kodaira-Iitaka dimension and multiplicity using intersection theory.

The paper explores curvature constraints on Kodaira dimension for specific almost Hermitian manifolds.

A Kodaira fibration is a compact, complex surface admitting a holomorphic submersion onto a complex curve, such that the fibers have nonconstant moduli. We consider Kodaira fibrations X with nontrivial invariant rational cohomology in degree 1, proving that if the dimension of the holomorphic invariants is 1 or 2, then…

Study of section conjecture analogues over complex numbers and Kodaira fibrations.

Paper extends Kodaira dimension's role in Yamabe invariant for most complex surfaces.

Study on the Kodaira dimension of real parallelizable manifolds with almost complex structures.

In this paper, by using analytical methods we obtain a generalization of the famous Kodaira embedding theorem.

Motivated by our conjecture of an earlier work predicting the degeneration at the second page of the Frölicher spectral sequence of any compact complex manifold supporting an SKT metric $ω$ (i.e. such that $\partial\bar\partialω=0$), we prove degeneration at $E_2$ whenever the manifold admits a Hermitian metric whose t…