Leonardo F. Cavenaghi

activity

20172026

most citedOn the geometry of some Equivariantly related manifolds

8 citations · 18 across the 23 of their papers we have counts for

collaborators

27 papers

math.AG2026

An atomic approach to Shokurov's conic-bundle conjecture

Leonardo F. Cavenaghi, Ludmil Katzarkov, Daniel Pomerleano +1

In this paper, we apply a weaker version of Hodge atoms to show that a standard conic bundle over a smooth complex projective rational surface $S$ is irrational if $|2K_S+Δ|\ne\emp…

math.DG2026

On the generalized cohomologies of almost abelian solvmanifolds

Mauro de Andrade Pinto, Letícia Camponês do Brasil Maia, Leonardo F. Cavenaghi +1

Generalized complex structures give rise to generalized Dolbeault, Bott--Chern and Aeppli cohomologies. We study these cohomologies for invariant generalized complex structures on…

math.AG2026

A quantum connection approach to rationality

Luiz Carazolli, Leonardo F. Cavenaghi, Ludmil Katzarkov +2

We extract rank and regularized exponents from cyclic generic factors of the quantum connection and show that these data persist under the birational comparisons considered here. A…

math.AG2026

On the atomic decomposition of complete intersection in flag varieties

Boris Alexeev, Leonardo F. Cavenaghi, Giovane Galindo +3

We develop a root-theoretic localization formalism for genus-zero Gromov--Witten invariants of flag varieties and of smooth zero loci of globally generated homogeneous vector bundl…

math.DG2026

On the generalized geometry of almost abelian solvmanifolds

Mauro de Andrade Pinto, Letícia Camponês do Brasil Maia, Leonardo F. Cavenaghi +1

We study left-invariant generalized complex structures on almost abelian Lie groups $G_{A}$ with Lie algebra $g_{A} = R e_{0} ⋉_{A} h$ , where $\mathfrak{h}…

hep-th2026

The Cohomology of Solvmanifold SYZ Mirrors

Leonardo F. Cavenaghi, Lino Grama, Ludmil Katzarkov +1

This paper investigates the geometric and cohomological properties of non-Kähler SYZ mirror symmetry for dual torus fibrations over solvmanifolds in the sense of Lau, Tseng and Yau…

math.AG2025

Atoms meet symbols

Leonardo F. Cavenaghi, Ludmil Katzarkov, Maxim Kontsevich

This paper introduces a novel framework for constructing invariants in $G$ -equivariant birational geometry by unifying two recent approaches: the theory of atoms recently developed…

math.AG2024

A Gromov-Witten approach to $G$ -equivariant birational invariants

Leonardo F. Cavenaghi, Lino Grama, Ludmil Katzarkov

In arXiv:2404.19088, we initiated a program linking birational invariants with smooth ones and offering new interpretations of classical invariants, such as the Kervaire-Milnor inv…

math.DG2024

A Geometric Realization of Spherical T-Duality via $⋆$ -Diagrams

Leonardo F. Cavenaghi, Lino Grama, Ludmil Katzarkov

We relate spherical T-duality for oriented linear $S^{3}$ -bundles over $S^{4}$ (the Milnor bundles $M_{m, n}$ , which are $S^{3}$ -principal exactly when $m = 0$ or…

math.DG2024★ 2 cited

Gromoll--Meyer's actions and the geometry of (exotic) spacetimes

Leonardo F. Cavenaghi, Lino Grama

Since the advent of new pairwise non-diffeomorphic structures on smooth manifolds, it has been questioned whether two topologically identical manifolds could admit different geomet…

math.DG2024

Hearing Exotic Smooth Structures

Leonardo F. Cavenaghi, João Marcos do Ó, Llohann D. Sperança

This paper explores the existence and properties of \emph{basic} eigenvalues and eigenfunctions associated with the Riemannian Laplacian on closed, connected Riemannian manifolds f…

math.DG2023

Singular Riemannian Foliations, variational problems and Principles of Symmetric Criticalities

Marcos M. Alexandrino, Leonardo F. Cavenaghi, Diego Corro +1

A singular foliation $F$ on a complete Riemannian manifold $M$ is called Singular Riemannian foliation (SRF for short) if its leaves are locally equidistant, e.g., the pa…

math.DG2023

The complete dynamics description of positively curved metrics in the Wallach flag manifold $SU (3) / T^{2}$

Leonardo F. Cavenaghi, Lino Grama, Ricardo M. Martins +1

The family of invariant Riemannian manifolds in the Wallach flag manifold $SU (3) / T^{2}$ is described by three parameters $(x, y, z)$ of positive real numbers. By rest…

math.DG2023

On the dynamics of positively curved metrics on $SU (3) / T^{2}$ under the homogeneous Ricci flow

Leonardo F. Cavenaghi, Lino Grama, Ricardo M. Martins

In this note, we show that the classical Wallach manifold $SU (3) / T^{2}$ -admits metrics of positive intermediate Ricci curvature $(Ric_{d} > 0)$ for $d = 1, 2,…

math.DG2023

Symmetric spaces as adjoint orbits and their geometries

Leonardo F. Cavenaghi, Carolina Garcia, Lino Grama +1

We realize specific classical symmetric spaces, like the semi-Kähler symmetric spaces discovered by Berger, as cotangent bundles of symmetric flag manifolds. These realizations ena…

math.DG2022

A curvature approach to fatness

Leonardo F. Cavenaghi, Lino Grama

This paper delves into the concept of ``fat bundles'' within Riemannian submersions. One explores the structural implications of fat Riemannian submersions, particularly focusing o…

math.DG2022

A note on the vertizontal curvature of fat bundles

Leonardo F. Cavenaghi

In his unpublished notes on fat bundles, W. Ziller poses a compelling question: given a fat principal $G$ -bundle $(P, g) \to (B, h)$ with $dim G = 3$ , and $g$ representing…

math.DG2022

Fatness and positive curvatures on Riemannian submersions

Leonardo F. Cavenaghi, Lino Grama, Llohann D. Sperança

Guided by rather counterintuitive properties of \emph{dual holonomy fields}, we introduce different notions of \emph{fatness} for Riemannian submersions. We introduce \emph{integra…

math.DG2021

Singular Riemannian Foliations and the prescribing scalar curvature problem

Marcos M. Alexandrino, Leonardo F. Cavenaghi

An orbit-like foliation is a singular foliation on a complete Riemannian manifold $M$ whose leaves are locally equidistant (i.e., a singular Riemannian foliation) and (transversely…

math.DG2021

The curvature of convex sum of metrics and applications

Leonardo F. Cavenaghi, Giovane Galindo, Llohann D. Sperança

In this note, we derive explicit formulae for the curvature of a convex sum of Riemannian metrics, $g_t = (1-t)g_0 + t g_1$. We study whether such a deformation can increase the…

math.DG2021

The $G$ -equivariant Kazdan--Warner problem

Leonardo F. Cavenaghi, João Marcos do Ó, Llohann D. Sperança

We establish an equivariant analogue of the Kazdan--Warner trichotomy for admissible scalar curvature functions. Let $M$ be a closed connected manifold of dimension $n \geq 3$ equip…

math.DG2020

A direct approach to prescribing scalar curvature on bundles

Leonardo Francisco Cavenaghi, Llohann Dallagnol Sperança

This note intends to demonstrate how to discuss scalar curvature functions' admissibility on bundles by directly applying some of the Kazdan--Warner results. Proofs of the concept…

math.DG2019★ 6 cited

Positive Ricci curvature on fiber bundles with compact structure group

Leonardo Francisco Cavenaghi, Llohann Dallagnol Sperança

The aim of this paper is to present a direct and simple proof of a result concerning the existence of metrics of positive Ricci curvature on the total space of fiber bundles with c…

math.DG2019

On Mean curvature flow of Singular Riemannian foliations: Non compact cases

Marcos M. Alexandrino, Leonardo F. Cavenaghi, Icaro Gonçalves

In this paper we investigate the mean curvature flow (MCF) of a regular leaf of a closed generalized isoparametric foliation as initial datum, generalizing previous results of Rade…

An atomic approach to Shokurov's conic-bundle conjecture

On the generalized cohomologies of almost abelian solvmanifolds

A quantum connection approach to rationality

On the atomic decomposition of complete intersection in flag varieties

On the generalized geometry of almost abelian solvmanifolds

The Cohomology of Solvmanifold SYZ Mirrors

Atoms meet symbols

A Gromov-Witten approach to G-equivariant birational invariants

A Geometric Realization of Spherical T-Duality via ⋆-Diagrams

Gromoll--Meyer's actions and the geometry of (exotic) spacetimes

Hearing Exotic Smooth Structures

Singular Riemannian Foliations, variational problems and Principles of Symmetric Criticalities

The complete dynamics description of positively curved metrics in the Wallach flag manifold SU(3)/T2

On the dynamics of positively curved metrics on SU(3)/T2 under the homogeneous Ricci flow

Symmetric spaces as adjoint orbits and their geometries

A curvature approach to fatness

A note on the vertizontal curvature of fat bundles

Fatness and positive curvatures on Riemannian submersions

Singular Riemannian Foliations and the prescribing scalar curvature problem

The curvature of convex sum of metrics and applications

The G-equivariant Kazdan--Warner problem

A direct approach to prescribing scalar curvature on bundles

Positive Ricci curvature on fiber bundles with compact structure group

On Mean curvature flow of Singular Riemannian foliations: Non compact cases

A Gromov-Witten approach to $G$ -equivariant birational invariants

A Geometric Realization of Spherical T-Duality via $⋆$ -Diagrams

The complete dynamics description of positively curved metrics in the Wallach flag manifold $SU (3) / T^{2}$

On the dynamics of positively curved metrics on $SU (3) / T^{2}$ under the homogeneous Ricci flow

The $G$ -equivariant Kazdan--Warner problem