Related papers: Explicit Examples of Strebel Differentials

We study the geometry of the smooth projective surfaces that are defined by Frobenius forms, a class of homogenous polynomials in prime characteristic recently shown to have minimal possible F-pure threshold among forms of the same degree.…

We study analytic integrable deformations of the germ of a holomorphic foliation given by $df=0$ at the origin $0 \in \mathbb C^n, n \geq 3$. We consider the case where $f$ is a germ of an irreducible and reduced holomorphic function. Our…

Though the uniformization theorem guarantees an equivalence of Riemann surfaces and smooth algebraic curves, moving between analytic and algebraic representations is inherently transcendental. Our analytic curves identify pairs of circles…

Let $\Omega$ be a strictly convex divisible subset of the $n$-dimensional real projective space which is not an ellipsoid. Even though $\partial\Omega$ is not $C^2$, Benoist showed that it is $C^{1+\alpha}$ for some $\alpha>0$, and Crampon…

We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…

Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated to real Riemann surfaces. Typical analytical problems in the numerical…

The partition function of an N=2 gauge theory in the Omega-background satisfies, for generic value of the parameter beta=-eps_1/eps_2, the, in general extended, but otherwise beta-independent, holomorphic anomaly equation of special…

Irreducible isoparametric foliations of arbitrary codimension q on complex projective spaces CP^n are classified, except if n=15 and q=1. Remarkably, there are noncongruent examples that pull back under the Hopf map to congruent foliations…

If $C$ is a smooth projective curve over an algebraically closed field $\mathbb{F}$ and $G$ is a subgroup of automorphisms of $C$, then $G$ acts linearly on the $\mathbb{F}$-vector space of holomorphic differentials…

In this paper we consider maps on the plane which are similar to quadratic maps in that they are degree 2 branched covers of the plane. In fact, consider for $\alpha$ fixed, maps $f_c$ which have the following form (in polar coordinates):…

We consider finite-dimensional complex Lie algebras admitting a periodic derivation, i.e., a nonsingular derivation which has finite multiplicative order. We show that such Lie algebras are at most two-step nilpotent and give several…

Let X be a minuscule Schubert variety and $\alpha$ a class of 1-cycle on X. In this article we describe the irreducible components of the scheme of morphisms of class $\alpha$ from a rational curve to X. The irreducible components are…

We consider the classical factorization problem of a third order ordinary differential operator $L-\lambda$, for a spectral parameter $\lambda$. It is assumed that $L$ is an algebro-geometric operator, that it has a nontrivial centralizer,…

In one of his posthumous papers, conserved in G\"ottingen, Riemann considers the derivatives of $\log\zeta(s)$ at the point $1/2$, giving explicit values for them. Around 2010 we shared Riemann's value of the second derivative with some…

Let F be the cubic field of discriminant -23 and O its ring of integers. Let Gamma be the arithmetic group GL_2 (O), and for any ideal n subset O let Gamma_0 (n) be the congruence subgroup of level n. In a previous paper, two of us (PG and…

In this paper, we prove that if $X$ is a Riemann surface of infinite analytic type and $[\mu ]_T$ is any element of Teichm\"uller space, then there exists $\mu_1 \in [\mu]_T$ so that $\mu_1$ is an infinitesimal Strebel point.

In this paper, we construct polynomial growth harmonic maps from once-punctured Riemann surfaces of any finite genus to any even-sided, regular, ideal polygon in the hyperbolic plane. We also establish their uniqueness within a class of…

Let X be a projective surface, let \sigma be an automorphism of X, and let L be a \sigma-ample invertible sheaf on X. We study the properties of a family of subrings, parameterized by geometric data, of the twisted homogeneous coordinate…

In this paper we consider mappings of jet spaces that preserve the module of canonical Pfaffian forms, but are not generally invertible. These mappings are called contact. A lemma on the prolongation of contact mappings is proved.…

We give an explicit example of a fibration $f \colon X \to Y$ between smooth projective varieties whose "orbifold base" $\Delta_f$ in the sense of Campana has the property that the induced morphism $X \to (Y, \Delta_f)$ is not a morphism of…