ON THE HYPERBOLICITY OF SURFACES OF GENERAL TYPE WITH SMALL c1
نویسندگان
چکیده
Surfaces of general type with positive second Segre number s2 := c1 − c2 > 0 are known by results of Bogomolov to be algebraically quasihyperbolic i.e. with finitely many rational and elliptic curves. These results were extended by McQuillan in his proof of the Green-Griffiths conjecture for entire curves on such surfaces. In this work, we study hyperbolic properties of minimal surfaces of general type with minimal c1, known as Horikawa surfaces. In principle these surfaces should be the most difficult case for the above conjecture as illustrate the quintic surfaces in P. Using orbifold techniques, we exhibit infinitely many irreducible components of the moduli of Horikawa surfaces whose very generic member has no rational curves or even is algebraically hyperbolic. Moreover, we construct explicit examples of algebraically hyperbolic and quasi-hyperbolic orbifold Horikawa surfaces.
منابع مشابه
On the hyperbolicity of surfaces of general type with small c 21
Surfaces of general type with positive second Segre number s2 := c 2 1 − c2 > 0 are known by the results of Bogomolov to be algebraically quasi-hyperbolic, that is, with finitely many rational and elliptic curves. These results were extended by McQuillan in his proof of the Green–Griffiths conjecture for entire curves on such surfaces. In this work, we study hyperbolic properties of minimal sur...
متن کاملOn the hyperbolicity of surfaces of general type with small c12
Surfaces of general type with positive second Segre number s2 := c 2 1 − c2 > 0 are known by results of Bogomolov to be algebraically quasihyperbolic i.e. with finitely many rational and elliptic curves. These results were extended by McQuillan in his proof of the Green-Griffiths conjecture for entire curves on such surfaces. In this work, we study hyperbolic properties of minimal surfaces of g...
متن کاملThe Role of Funnels and Punctures in the Gromov Hyperbolicity of Riemann Surfaces
We prove results on geodesic metric spaces which guarantee that some spaces are not hyperbolic in the Gromov sense. We use these theorems in order to study the hyperbolicity of Riemann surfaces. We obtain a criterion on the genus of a surface which implies non-hyperbolicity. We also include a characterization of the hyperbolicity of a Riemann surface S∗ obtained by deleting a closed set from on...
متن کاملSemi-hyperbolicity and Hyperbolicity
We prove that for C1-diffeomorfisms semi-hyperbolicity of an invariant set implies its hyperbolicity. Moreover, we provide some exact estimations of hyperbolicity constants by semi-hyperbolicity ones, which can be useful in strict numerical computations.
متن کاملHyperbolicity of the family $f_c(x)=c(x-frac{x^3}{3})$
The aim of this paper is to present a proof of the hyperbolicity of the family $f_c(x)=c(x-frac{x^3}{3}), |c|>3$, on an its invariant subset of $mathbb{R}$.
متن کامل