19 papers
The topology of Kähler manifolds and 1-forms without zeros
Maurício Corrêa, János Kollár, Stefan Schreieder +1
We study how the topology and geometry of a compact Kähler manifold relate to the zeros of its one-forms. We determine all implications among several closely related conditions. In…
Supermoduli spaces are non-projected in every genus
Mauricio Corrêa, Ron Donagi, Simone Noja
We prove that, for every genus , the primary obstruction of each parity component of the moduli superstack of smooth unpunctured super Riemann surfaces is nonzero, both al…
Transverse analytic envelopes and integrability
Maurício Corrêa, José Seade
We associate normal toric transverse analytic envelopes with the singular orbits of diagonal holomorphic actions, and construct their canonical flat transport. At independent singu…
Homology fiber bundles of varieties, that are not topological fiber bundles
Maurício Corrêa, János Kollár
We construct flat, projective morphisms that are -homology fiber bundles, have a smooth total space, but are not smooth. This disproves one of the conjectures of the sec…
Invisible singularities in complex algebraic geometry
Maurício Corrêa, János Kollár, Stefan Schreieder +1
We construct morphisms between smooth complex projective varieties that have singular fibers, but look topologically smooth. We use this to give negative answers to the following f…
Shifted Poisson unfoldings and quantum anomalies
Mauricio Corrêa, Simone Noja
Families of classical field theories often depend on geometric parameters. A basic question is whether the corresponding classical observables can be compared by flat parallel tran…
Foliated and Mather-Jacobian discrepancies via tangential arcs
Maurício Corrêa
This article develops a tangential arc-space approach to foliated discrepancies for logarithmic simple co-rank one foliations on threefolds, relative to a fixed invariant normal cr…
Compactified supermoduli space is almost never projected
Mauricio Corrêa, Simone Noja
We settle the projectedness problem for the compactified unpunctured supermoduli stack in every genus at least two. In genus two, the odd component is split, whereas the even compo…
Stacky geometry and logarithmic topology of transversely affine foliations
Pedro Barbassa, Gabriel Barbosa, Maurício Corrêa
We study the stacky and logarithmic-topological structures associated with transversely affine affine foliations. To such a foliation we attach its holonomy group and the correspon…
Formal moduli and the splitting theory of supermanifolds
Mauricio Corrêa, Simone Noja
We develop a formal moduli theory for the splitting problem of complex supermanifolds. Starting from Green's obstruction tower, we construct a finite-step filtered dg Lie algebra w…
The logarithmic leaf complex and foliated d-semistability
Mauricio Corrêa, Pablo Perrella, Sebastián Velazquez
We study holomorphic foliations on normal crossings varieties arising as semistable degenerations. We do so by we exploring the notion of foliated d-semistability using the languag…
Excess logarithmic residues for foliations by curves and applications
Alana Cavalcante, Maurício Corrêa, Fernando Lourenço +1
We introduce excess logarithmic residues for one-dimensional holomorphic foliations tangent to a divisor. They arise from the comparison between the logarithmic normal sheaf and th…
Log-Conformal Projective Manifolds
Maurício Corrêa, Alex Massarenti
Let be a smooth complex projective simple normal crossing pair of dimension endowed with an everywhere nondegenerate logarithmic conformal tensor. If is no…
Geometry of the Donaldson-Friedman Pushout: Twistor degenerations and instanton charge
Amedeo Altavilla, Maurício Corrêa
We study the Donaldson-Friedman semistable twistor degeneration by combining the scheme-theoretic geometry of its Ferrand pushout with the logarithmic topology of its Kato-Nakayama…
A categorical and algebro-geometric theory of localization
Mauricio Corrêa, Simone Noja
We study cohomology classes whose restriction to the complement of a closed subset vanishes. The localisation sequence shows that their lifts to cohomology with support form a tors…
Log Bott localization with non-isolated lci zero varieties
Maurício Corrêa, Elaheh Shahsavaripour
We establish a logarithmic Bott localization formula for global holomorphic sections of on a compact complex manifold with simple normal crossings divisor . T…
A Čech--Stokes Pushout Groupoid: a Log/Kummer Betti Presenter for Stokes Torsors
Mauricio Corrêa
We give an explicit Betti presentation of the Stokes torsors attached to meromorphic flat connections of prescribed irregular type along a simple normal crossings divisor, at fixed…
On the connectedness of the singular set of holomorphic foliations
Omegar Calvo-Andrade, Maurício Corrêa, Marcos Jardim +1
Let be a singular holomorphic foliation of dimension on a projective -manifold . Assume that the determinant of the normal sheaf of is ample…
Indices and residues: from Poincaré-Hopf to Baum-Bott, and Marco Brunella
Maurício Corrêa, José Seade
In this expository article, we study and discuss invariants of vector fields and holomorphic foliations that intertwine the theories of complex analytic singular varieties and sing…