Related papers: On elliptic modular foliations

We consider a finite composition of generalized H\'{e}non mappings $\mathfrak{f}:\mathbb{C}^2\to\mathbb{C}^2$ and its Green function $\mathfrak{g}^+:\mathbb{C}^2\to\mathbb{R}_{\ge 0}$ (see Section 2). It is well known that each level set…

In a recent paper we constructed a family of foliated 2-complexes of thin type whose typical leaves have two topological ends. Here we present simpler examples of such complexes that are, in addition, symmetric with respect to an involution…

We study compatible and associated metrics for a contact-symplectic pair $(\eta , \omega)$ on a manifold. We show that the integral curves of the Reeb vector field are geodesics for any compatible metric. We prove that all associated…

Nikulin and Vinberg proved that there are only a finite number of lattices of rank $\geq 3$ that are the N\'eron-Severi group of projective K3 surfaces with a finite automorphism group. The aim of this paper is to provide a more geometric…

We show that a smooth 1-parameter family of foliations by circles of a closed 3-manifold, deforming the foliation whose leaves are the fibers of a circle bundle, is trivial, i.e. all the foliations of the family arise from circle bundles…

We show that, for any regular Poisson manifold, there is an injective natural linear map from the first leafwise cohomology space into the first Poisson cohomology space which maps the Reeb class of the symplectic foliation to the modular…

Given a canonical algebraically integrable foliation on a klt projective variety, we study the variation of the ample models of the associated adjoint foliated structures with respect to the parameter. When the foliation is of general type,…

We study the boundary $L_t$ of the Milnor fiber for the reduced holomorphic germs $f:(\Bbb C^3,0) \rightarrow (\Bbb C,0)$ having a non-isolated singularity at $0$. We prove that $L_t$ is a graph manifold by using a new technique of…

Let $\mathcal{F}$ be written as $ f^{*}\mathcal{G}$, where $\mathcal{G}$ is a foliation in $ {\mathbb P^2}$ with three invariant lines in general position, say $(XYZ)=0$, and $f:{\mathbb P^n}--->{\mathbb P^2}$,…

The purpose of this work is to obtain the degree of the exceptional component of the space of holomorphic foliations of degree two and codimension one in P^3. We construct a parameter space as an explicit fiber bundle over the variety of…

Let $E$ be an ordinary elliptic curve over a finite field and $g$ be a positive integer. Under some technical assumptions, we give an algorithm to span the isomorphism classes of principally polarized abelian varieties in the isogeny class…

It is a classical fact going back to F. Klein that an elliptic curve $E$ over $\bar{\mathbb{Q}}$ is defined by a homogeneous polynomial in $3$ variables with coefficients in $\mathbb{Q}(j_{E})$, where $j_{E}$ is the $j$-invariant of $E$,…

We prove that the open unit ball $\mathbb{B}_n$ of $\mathbb{C}^n$ $(n\ge 2)$ admits a nonsingular holomorphic foliation $\mathcal F$ by closed complex hypersurfaces such that both the union of the complete leaves of $\mathcal F$ and the…

A smooth foliation of a Riemannian manifold is metric when its leaves are locally equidistant and is homogenous when its leaves are locally orbits of a Lie group acting by isometries. Homogenous foliations are metric foliations, but metric…

We study degree 2 and 4 elliptic subcovers of hyperelliptic curves of genus 3 defined over $\mathbb C$. The family of genus 3 hyperelliptic curves which have a degree 2 cover to an elliptic curve $E$ and degree 4 covers to elliptic curves…

We extend the unpublished work of M. Handel and R. Miller on the classification, up to isotopy, of endperiodic automorphisms of surfaces. We give the Handel-Miller construction of the geodesic laminations, give an axiomatic theory for…

We make explicit computations in the formal symplectic geometry of Kontsevich and determine the Euler characteristics of the three cases, namely commutative, Lie and associative ones, up to certain weights.From these, we obtain some…

The Kimura 3-parameter model on a tree of n leaves is one of the most used in phylogenetics. The affine algebraic variety W associated to it is a toric variety. We study its geometry and we prove that it is isomorphic to a geometric…

In this paper, we address one of the most basic and fundamental problems in the theory of foliations and ODEs, the topological invariance of the algebraic multiplicity of a holomorphic foliation. For instance, we prove an adapted version of…

Elliptic modular graph forms (eMGFs) are non-holomorphic modular forms depending on a modular parameter $\tau$ of a torus and marked points $z$ thereon. Traditionally, eMGFs are constructed from nested lattice sums over the discrete momenta…