Related papers: Foliations with vanishing Chern classes

We study twisted ideal sheaves of small length on an irreducible principally polarized abelian surface (T,l). Using Fourier-Mukai techniques we associate certain jumping schemes to such sheaves and completely classify such loci. We give…

Let $M$ be a finite dimensional topological aspherical manifold whose universal cover is ${\bf R}^n$. In this paper, we study $Aff(M)$, the subgroup of the group of homeomorphisms of $M$, whose elements can be lifted to affine…

A singular foliation is called a singular Riemannian foliation (SRF) if every geodesic that is perpendicular to one leaf is perpendicular to every leaf it meets. A typical example is the partition of a complete Riemannian manifold into…

We give a complete description of partially wrapped Fukaya categories of graded orbifold surfaces with stops. We show that a construction via global sections of a natural cosheaf of A$_\infty$ categories on a Lagrangian core of the surface…

Classification results for complex Riemannian foliations are obtained. For open subsets of irreducible Hermitian symmetric spaces of compact type, where one has explicit control over the curvature tensor, we completely classify such…

Let $\mathcal{F}$ be a codimension one holomorphic foliation in $\mathbb{P}^n$, $n\geq 2$, leaving invariant a real-analytic Levi-flat hypersurface $M$ with regular part $M^{*}$. Then every leaf of $\mathcal{F}$ outside $\overline{M^{*}}$…

In this paper, we study homogeneous convex foliations on the complex projective plane $\mathbb{P}^2$. A foliation is called convex if all of its leaves, except straight lines, have no inflection points, and such foliations form a Zariski…

An abelian cover is a finite morphism $X\to Y$ of varieties which is the quotient map for a generically faithful action of a finite abelian group $G$. Abelian covers with $Y$ smooth and $X$ normal were studied in…

The purpose of this paper is to introduce a Zariski-like topology on the spectrum of all proper ideals of a ring. We show that the space is T_0, quasi-compact, and every irreducible closed subset has a unique generic point. Furthermore,…

A holomorphic foliation is defined as an integrable coherent subsheaf of the tangent sheaf. The structure of the leaves around a singularity is read off from the structure of the stalks. This was done by Baum when the dimension of the…

We construct the functional integral of Abelian Chern-Simons theory with toral gauge group $\mathbb T=\mathfrak t/\Lambda \cong U(1)^n$ at level $K$, where $K:\Lambda\times\Lambda\to\mathbb Z$ is an even, integral, nondegenerate symmetric…

Let G be a smooth algebraic group acting on a variety X. Let F and E be coherent sheaves on X. We show that if all the higher Tor sheaves of F against G-orbits vanish, then for generic g in G, the sheaf Tor^X_j(gF, E) vanishes for all j >0.…

In the context of uniformisation problems, we study projective varieties with klt singularities whose cotangent sheaf admits a projectively flat structure over the smooth locus. Generalising work of Jahnke-Radloff, we show that torus…

We find conditions which ensure that the topological complexity of a closed manifold $M$ with abelian fundamental group is nonmaximal, and see through examples that our conditions are sharp. This generalizes results of Costa and Farber on…

We establish a correspondence between simplicial fans, not necessarily rational, and certain foliated compact complex manifolds called LVMB-manifolds. In the rational case, Meersseman and Verjovsky have shown that the leaf space is the…

We begin a systematic investigation of derived categories of smooth projective toric varieties defined over an arbitrary base field. We show that, in many cases, toric varieties admit full exceptional collections. Examples include all toric…

We define the twisted affine Yangian of type $C$ and construct surjective homomorphisms from twisted affine Yangians of type $C$ to the universal enveloping algebra of the rectangular $W$-algebra associated with $\mathfrak{so}(ln)$ and a…

Given a reflexive sheaf on a mildly singular projective variety, we prove a flatness criterion under certain stability conditions. This implies the algebraicity of leaves for sufficiently stable foliations with numerically trivial canonical…

This work concerns the problem of relating characteristic numbers of one-dimensional holomorphic foliations of P^n to those of algebraic varieties invariant by them. More precisely: if M is a connected complex manifold, a one-dimensional…

Let $A$ be an abelian variety in a field of characteristic $0$. We prove that the expansion of $A$ by a generic divisible subgroup of $A$ with the same torsion exists provided $A$ has few algebraic endomorphisms, namely…