Related papers: A factorisation theorem for curve with vanishing s…

Let $C$ be a smooth projective curve, and let $J$ be its Jacobian. We prove vanishing criteria for the Ceresa cycle $\kappa(C) \in \mathrm{CH}_1(J)\otimes \mathbb{Q}$ in the Chow group of 1-cycles on $J$. Namely, $(A)$ If…

In 1977 P.Yang asked whether there exist complete immersed complex submanifolds g : M^k --> C^N with bounded image. A positive answer is known for holomorphic curves (k=1) and partial answers are known for the case when k>1. The principal…

Let $C$ be a $4$-cover of an elliptic curve $E$, written as a quadric intersection in $\mathbb{P}^3$. Let $E'$ be another elliptic curve with $4$-torsion isomorphic to that of $E$. We show how to write down the $4$-cover $C'$ of $E'$ with…

Building on the work of the fourth author in math.AG/9904074, we prove the weak factorization conjecture for birational maps in characteristic zero: a birational map between complete nonsingular varieties over an algebraically closed field…

This article generalizes the result of Katzarkov and Ramachandran from algebraic surfaces to K\"ahler surfaces. We follow their argument to prove the holomorphic convexity of a reductive Galois covering over a compact K\"ahler surface which…

The following pullback problem will be considered. Given a finite holomorphic map germ $\phi : (\mathbb{C}^{n}, 0) \to (\mathbb{C}^{n}, 0)$ and an analytic germ $X$ in the target, if the preimage $Y = \phi^{-1}(X)$, taken with the reduced…

Given a connected dense Zariski open set of a compact K\"ahler manifold $U$, we address the general problem of the existence of surjective holomorphic maps ${F:U\to C}$ to smooth complex quasi-projective curves from properties of…

We consider a map $F$ of class $C^r$ with a fixed point of parabolic type whose differential is not diagonalizable and we study the existence and regularity of the invariant manifolds associated with the fixed point using the…

The purpose of this paper is to present a solution to perhaps the final remaining case in the line of study concerning the generalization of Forelli's theorem on the complex analyticity of the functions that are: (1) $\mathcal{C}^\infty$…

We use contact fiber sums of open book decompositions to define an infinite hierarchy of filling obstructions for contact 3-manifolds, called planar k-torsion for nonnegative integers k, all of which cause the contact invariant in Embedded…

We show that if f: X --> Y is a finite, separable morphism of smooth curves defined over a finite field F_q, where q is larger than an explicit constant depending only on the degree of f and the genus of X, then f maps X(F_q) surjectively…

In this paper, we revisit local invariants (G\'omez-Mont-Seade-Verjovsky, variation, Camacho-Sad and Baum-Bott indices) associated with singular holomorphic foliations on $(\mathbb{C}^2 , 0)$ and we provide semi-global formulas for them in…

For $n\geq 3$, let $M$ be an $(n+r)$-dimensional irreducible Hermitian symmetric space of compact type and let $\mathcal{O}_M(1)$ be the ample generator of $Pic(M)$. Let $Y=H_1\cap\dots\cap H_r$ be a smooth complete intersection of…

We solve a problem posed by Cardinali and Sastry [2] about factorization of $2$-covers of finite classical generalized quadrangles. To that end, we develop a general theory of cover factorization for generalized quadrangles, and in…

We discuss factorization of the Dyson--Schwinger equations using the Lie- and Hopf algebra of graphs. The structure of those equations allows to introduce a commutative associative product on 1PI graphs. In scalar field theories, this…

Let $C\subset \mathbb P^r$ be an integral projective curve. We define the speciality index $e(C)$ of $C$ as the maximal integer $t$ such that $h^0(C,\omega_C(-t))>0$, where $\omega_C$ denotes the dualizing sheaf of $C$. In the present paper…

Any traversally generic vector flow on a compact manifold $X$ with boundary leaves some residual structure on its boundary $\d X$. A part of this structure is the flow-generated causality map $C_v$, which takes a region of $\d X$ to the…

Let C be a 2-connected Gorenstein curve either reduced or contained in a smooth algebraic surface and let S be a subcanonical cluster (i.e. a 0-dim scheme such that the space H^0(C, I_S K_C) contains a generically invertible section). Under…

We study infinite superelliptic curves as translation surfaces and explore their Veech groups. These objects are branched covering of the complex plane with branching over infinitely many points. We provide a criterion for isomorphism…

Let $G$ be a finitely generated group acting faithfully and properly discontinuously by homeomorphisms on a planar surface $X \subseteq \mathbb{S}^2$. We prove that $G$ admits such an action that is in addition co-compact, provided we can…