Related papers: On Segre-degenerate Levi-flat hypervarieties

Let $\mathcal S\to\mathbb A^1$ be a smooth family of surfaces whose general fibre is a smooth surface of $\mathbb P^3$ and whose special fibre has two smooth components, intersecting transversally along a smooth curve $R$. We consider the…

We study equisingular deformation problems for curves and surfaces in algebraic families, with particular emphasis on situations where nodal behavior is no longer generic. Extending classical Severi theory, we develop deformation--theoretic…

An exp-algebraic curve consists of a compact Riemann surface $S$ together with $n$ equivalence classes of germs of meromorphic functions modulo germs of holomorphic functions, $\HH = \{ [h_1], \cdots, [h_n] \}$, with poles of orders $d_1,…

As set systems, hypergraphs are omnipresent and have various representations ranging from Euler and Venn diagrams to contact representations. In a geometric representation of a hypergraph $H=(V,E)$, each vertex $v\in V$ is associated with a…

Let $C$ be a curve of genus two. We denote by $SU_C(3)$ the moduli space of semi-stable vector bundles of rank 3 and trivial determinant over $C$, and by $J^d$ the variety of line bundles of degree $d$ on $C$. In particular, $J^1$ has a…

The deformation problem for pseudoholomorphic curves and related geometrical properties of the total moduli space of pseudoholomorphic curves are studied. A sufficient condition for the saddle point property of the total moduli space is…

The bounded derived category of coherent sheaves on a smooth projective variety is known to be equivalent to the triangulated category of perfect modules over a DG algebra. DG algebras, arising in this way, have to satisfy some compactness…

Let X be an irreducible hypersurface in $\mathbb{P}^n$ of degree $d\geq 3$ with only isolated semi-weighted homogeneous singularities, such that $exp(\frac{2\pi i}{k})$ is a zero of the Alexander polynomial. Then we show that the…

In this paper, we consider local holomorphic mappings f: M\to M' between real algebraic CR generic manifolds (or more generally, real algebraic sets with singularities) in the complex euclidean spaces of different dimensions and we search…

We prove finite jet determination results for smooth CR embeddings which are of constant degeneracy, using the method of complete systems. As an application, we derive a reflection principle for mappings between a Levi-nondegenerate…

Let $X$ be a connected open Riemann surface. Let $Y$ be an Oka domain in the smooth locus of an analytic subvariety of $\mathbb C^n$, $n\geq 1$, such that the convex hull of $Y$ is all of $\mathbb C^n$. Let $\mathscr O_*(X, Y)$ be the space…

We study pseudoholomorphic discs with boundaries attached to a real hypersurface in an almost complex manifold. We give sufficient conditions for filling a one sided neighborhood of the hypersurface by the discs.

We consider polynomials expressing the cohomology classes of subvarieties of products of projective spaces, and limits of positive real multiples of such polynomials. We study the relation between these covolume polynomials and Lorentzian…

Given a complex affine hypersurface with isolated singularity determined by a homogeneous polynomial, we identify the noncommutative Hodge structure on the periodic cyclic homology of its singularity category with the classical Hodge…

Inspired by an article of R. Bryant on holomorphic immersions of unit disks into Lorentzian CR manifolds, we discuss the application of Cartan's method to the question of the existence of bi-disk $\mathbb{D}^{2}$ in a smooth $9$-dimensional…

This article deals with the existence of hypersurfaces minimizing general shape functionals under certain geometric constraints. We consider as admissible shapes orientable hypersurfaces satisfying a so-called reach condition, also known as…

In this article we extend the notion of determinantal representation of hypersurfaces to the determinantal representation of sections of the determinant line bundle of a vector bundle. We give several examples, and prove some necessary…

Let X be a complex manifold and c a simple closed curve in X. We address the question: What conditions on c ensure the existence of a 1-dimensional complex subvariety V with boundary c in X. When X = C^n, an answer to this question involves…

The space of de Rham currents supported in finitely many points in a Lie group $G$ has the structure of a filtered differential graded Hopf algebra. The product is given by convolution of compactly supported currents, and the co-product…

Recently, Marian-Oprea-Pandharipande established (a generalization of) Lehn's conjecture for Segre numbers associated to Hilbert schemes of points on surfaces. Extending work of Johnson, they provided a conjectural correspondence between…