14 papers · 1 filter
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…