Related papers: Algebraic Levi-flat hypervarieties in complex proj…

In this paper, necessary and sufficient criteria for the Jacobian ideal of a reduced hypersurface with isolated singularity to be of linear type, are presented. We prove that the gradient ideal of a reduced projective plane curve with…

Degenerations of Lie algebras of meromorphic vector fields on elliptic curves (i.e. complex tori) which are holomorphic outside a certain set of points (markings) are studied. By an algebraic geometric degeneration process certain…

We study the problem of classifying local projective structures in dimension two having non trivial Lie symmetries. In particular we obtain a classification of flat projective structures having positive dimensional Lie algebra of projective…

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 $\overline{M^{*}}$…

We show that the isolated invariant branches globalize to algebraic curves, when we consider weak toric type complex hyperbolic foliations on projective toric ambient surfaces. To do it, we pass through a characterization of weak toric type…

We survey recent developments in the study of perverse sheaves on semi-abelian varieties. As concrete applications, we discuss various obstructions on the homotopy type of complex algebraic manifolds (expressed in terms of their cohomology…

In this paper, we introduce pre-Lie and pre-Leibniz superalgebras, which generalize pre-Lie and pre-Leibniz algebras to the super setting. Additionally, we define a Levi-Civita product associated with a symmetric non-degenerate bilinear…

We bound the codimension of components of the nonabelian Hodge loci in the relative de Rham moduli space over $\shm_{g,n}$ in terms of the rank and level of a complex variation of Hodge structure. If the rank is $r$ and the level is $\ell$,…

Let $F(z)=\mathcal{R}e(P(z)) + h.o.t$ be such that $M=(F=0)$ defines a germ of real analytic Levi-flat at $0\in\mathbb{C}^{n}$, $n\geq{2}$, where $P(z)$ is a homogeneous polynomial of degree $k$ with an isolated singularity at…

We give a criterion for certain generic nondegenerate surfaces in a fake weighted projective $3$-space to have Picard number $>1$. These algebraic surfaces are of general type. We do this by considering degenerations (along an edge),…

Let ${\mathfrak C}_{2,1}$ be the class of connected 5-dimensional CR-hypersurfaces that are 2-nondegenerate and uniformly Levi degenerate of rank 1. We show that the CR-structures in ${\mathfrak C}_{2,1}$ are reducible to…

We stratify families of projective and very affine hypersurfaces according to their topological Euler characteristic. Our new algorithms compute all strata using algebro-geometric techniques. For very affine hypersurfaces, we investigate…

We study the local Killing Lie algebra of meromorphic almost rigid geometric structures on complex manifolds. This leads to classification results for compact complex manifolds bearing holomorphic rigid geometric structures.

We study the algebraic hyperbolicity of the complement of very general degree $2n$ hypersurfaces in P^n. We prove the Algebraic Green-Griffiths-Lang Conjecture for these complements, and in the case of the complement of a quartic plane…

We construct the deformation functor associated with a pair of morphisms of differential graded Lie algebras, and use it to study infinitesimal deformations of holomorphic maps of compact complex manifolds. In particular, using L-infinity…

We introduce new invariant tensors in CR structures which can be viewed as higher order Levi forms. Using the second and third order tensors, we give a complete formal normal form (in the sense of Chern-Moser) for a real hypersurface at a…

All results concern characteristic 2. Two procedures that to every simple Lie algebra assign simple Lie superalgebras, most of the latter new, are offered. We prove that every simple finite-dimensional Lie superalgebra is obtained as the…

In this paper we study sectional curvature of invariant hyper-Hermitian metrics on simply connected 4-dimensional real Lie groups admitting invariant hypercomplex structure. We give the Levi-Civita connections and explicit formulas for…

We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide a characterization of the focal set in terms of its second fundamental form and determine the principal…

We study singular hypersurfaces in tensor multi-scalar theories of gravity. We derive in a distributional and then in an intrinsic way, the general equations of junction valid for all types of hypersurfaces, in particular for lightlike…