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papers

Publications (8)

math.DG2021

Fibrations in semi-toric and generalized complex geometry

Gil R. Cavalcanti, Ralph L. Klaasse, Aldo Witte

This paper studies the interplay between self-crossing boundary Lefschetz fibrations and generalized complex structures. We show that these fibrations arise from the moment maps in…

math.DG2025

$b^{k}$ -algebroids and the variety of foliation jets

Francis Bischoff, Ãlvaro del Pino, Aldo Witte

We introduce and classify singular foliations of $b^{k + 1}$ -type, which formalize the properties of vector fields that are tangent to a submanifold $W \subset M$ to order $k$ . When…

math.DG2022

Regularisation of Lie algebroids and Applications

Ãlvaro del Pino, Aldo Witte

We describe a procedure, called regularisation, that allows us to study geometric structures on Lie algebroids via foliated geometric structures on a manifold of higher dimension.…

math.DG2025

Non-principal T-duality, generalized complex geometry and blow-ups

Gil R. Cavalcanti, Aldo Witte

We extend the notion of T-duality to manifolds endowed with non-principal torus actions. The singularities of the torus action are controlled by a certain Lie algebroid, called the…

math.DG2026

Polynomial degeneration and the Poisson geometry of truncated polynomials

Francis Bischoff, Aldo Witte

The paper introduces a formalism for geometric structures that degenerate polynomially along a hypersurface and applies it to Poisson geometry, constructing generically symplectic…

#poisson geometry#symplectic degeneration#truncated polynomial groups#character varieties

math.DG2020

Self-crossing stable generalized complex structures

Gil R. Cavalcanti, Ralph L. Klaasse, Aldo Witte

We extend the notion of (smooth) stable generalized complex structures to allow for an anticanonical section with normal self-crossing singularities. This weakening not only allows…

math.DG2021

The cohomology of the elliptic tangent bundle

Aldo Witte

In this note we compute the cohomology of the elliptic tangent bundle, a Lie algebroid used to describe singular symplectic forms arising from generalized complex geometry.

math.DG2023

Jets of foliations and $b^{k}$ -algebroids