Riemann surface are 2-manifolds with complex analytical structure, and are thus a meeting ground for topology and complex analysis. Cohomology with coefficients in the sheaf of holomorphic functions is an important tool in the study of Riemann surfaces. This algebraic structure is interesting

In this paper we shall study a special class of solutions of the self-dual Yang-Mills equations. The original self-duality equations which arose in mathematical physics were defined on Euclidean 4-space. The physically relevant solutions were the ones with finite action—the so-called 'instantons'. The same equations may be

Propósito: Recientemente se ha hipotetizado que la proteína nuclear p63 es el primer marca-dor de las células madres del epitelio corneal durante el desarrollo. La presente publicación determina la localización de las células queratolimbales madres del epitelio corneal por el patrón de expresión p63 en la superficie ocular. Métodos: Se usó tejido queratolimbal humano para detectar por inmunohistoquimia el patrón de expresión de la proteína p63. Se desarrolló la hibridización in situ bidireccional para confirmar la expresión p63 mRNA en el anillo queratolimbal. Resultados: La proteína p63 y ARNm se expresaron sólo en los núcleos de la capa basal de las células epiteliales limbales. Conclusión: De acuerdo con nuestros hallazgos, la proteína p63 localizada en la células basa-les del epitelio queratolimbal es un buen marcador para detectar las células madres del epi-telio corneal. La p63 podría utilizarse en práctica clínica para determinar la actividad de las células madres del epitelio corneal. Palabras clave: P63, limbo corneal, células madre, epitelio corneal. SUMMARY

A Riemann surface (or smooth complex curve) is a complex manifold of dimension one. We will restrict to compact Riemann surfaces. It is a theorem that compact Riemann surfaces are the same as smooth projective curves, this is, closed one dimensional complex manifolds in P n defined by a system

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We derive closed formulas for the Arakelov-Green function and the Faltings delta-invariant of a compact Riemann surface.

Partially supported by the NSF Grant DMS-0072534In this paper, we address the following question: What does a typical compact Riemann surface of large genus look like geometrically? By a Riemann surface, we mean an oriented surface with a complete, finite-area metric of constant curvature-1

this paper, we address the following question: given a natural number g, how many Riemann surfaces S 1 ; : : : ; S k of genus g can there be such that S 1 ; : : : ; S k all share the same spectrum of the Laplacian?

These are notes on the theory of super Riemann surfaces and their moduli spaces, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNS formalism.

If a bordered Riemann surface admits an injective holomorphic immersion into C², then its interior admits a proper holomorphic embedding into C².