Singular foliations with trivial canonical class
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Codimension one foliations of degree three on projective spaces
RC da Costa, R Lizarbe, JV Pereira - Bulletin des Sciences Mathématiques, 2022 - Elsevier
We establish a structure theorem for degree three codimension one foliations on projective
spaces of dimension n≥ 3, extending a result by Loray, Pereira, and Touzet for degree three …
spaces of dimension n≥ 3, extending a result by Loray, Pereira, and Touzet for degree three …
On the singular scheme of split foliations
We prove that the tangent sheaf of a codimension-one locally free distribution splits as a
sum of line bundles if and only if its singular scheme is arithmetically Cohen-Macaulay. In …
sum of line bundles if and only if its singular scheme is arithmetically Cohen-Macaulay. In …
On degeneracy schemes of maps of vector bundles and applications to holomorphic foliations
C Araujo, M Corrêa - Mathematische Zeitschrift, 2014 - Springer
In this paper we provide sufficient conditions for maps of vector bundles on smooth
projective varieties to be uniquely determined by their degeneracy schemes. We then …
projective varieties to be uniquely determined by their degeneracy schemes. We then …
Holomorphic foliations of degree two and arbitrary dimension
M Corrêa, A Muniz - arxiv preprint arxiv:2207.12880, 2022 - arxiv.org
Let $\mathscr {F} $ be a holomorphic foliation of degree $2 $ on $\mathbb {P}^ n $ with
dimension $ k\geq 2$. We prove that either $\mathscr {F} $ is algebraically integrable, or …
dimension $ k\geq 2$. We prove that either $\mathscr {F} $ is algebraically integrable, or …
ON THE SINGULAR SCHEME OF CODIMENSION ONE HOLOMORPHIC FOLIATIONS IN ℙ3
In this work, we begin by showing that a holomorphic foliation with singularities is reduced if
and only if its normal sheaf is torsion-free. In addition, when the codimension of the singular …
and only if its normal sheaf is torsion-free. In addition, when the codimension of the singular …
Stability of logarithmic differential one-forms
This article deals with the irreducible components of the space of codimension one foliations
in a projective space defined by logarithmic forms of a certain degree. We study the …
in a projective space defined by logarithmic forms of a certain degree. We study the …
A characterization of diagonal Poisson structures
The degeneracy locus of a generically symplectic Poisson structure on a Fano manifold is
always a singular hypersurface. We prove that there exists just one family of generically …
always a singular hypersurface. We prove that there exists just one family of generically …
Families of distributions and Pfaff systems under duality
F Quallbrunn - arxiv preprint arxiv:1305.3817, 2013 - arxiv.org
A singular distribution on a non-singular variety $ X $ can be defined either by a subsheaf $
D $ of the tangent sheaf, or by the zeros of a subsheaf $ D^ 0$ of the sheaf of 1-forms …
D $ of the tangent sheaf, or by the zeros of a subsheaf $ D^ 0$ of the sheaf of 1-forms …
Codimension one foliations in positive characteristic
CODIMENSION ONE FOLIATIONS IN POSITIVE CHARACTERISTIC Page 1 J. Inst. Math.
Jussieu (2024), 23(4), 1705–1750 doi:10.1017/S1474748023000361 1705 CODIMENSION ONE …
Jussieu (2024), 23(4), 1705–1750 doi:10.1017/S1474748023000361 1705 CODIMENSION ONE …