### Revista Colombiana de Matemáticas

Volumen 41 [2] (2007)Páginas 371 - 380

The cohomology solution and the index theorem on ring surfaces of genus g

Changfeng Xue,Wenchang Tan
Yancheng Institute of Technology, Yancheng, Jiangsu 224003, P.R. China

Resumen.En este artículo se presentan algunas propiedades básicas de la solución cohomológica para superficies sobre anillos de género $g$ y se obtienen los teoremas de Dolbeault y Serre para el operador $\bar\partial = \frac{\partial }{{\partial \bar z}}d\bar z$. Se discute el teorema del índice para tales superficies. \keywords{Superficie sobre anillos, cohomología, género, índice.} \end{secondabstract}

Abstract. In this paper, some basic properties of the cohomology solution on ring surfaces of genus $g$ are presented, and the theorem of Dolbeault and the theorem of Serre for the operator $\bar\partial = \frac{\partial }{{\partial \bar z}}d\bar z$ are obtained. The index theorem on such ring surfaces of genus $g$ is also discussed.

* This work was supported by National Natural Science Foundation of China (grant numbers: 10572006, 10632010).

Palabras claves. Ring surface, cohomology, genus, index.

Codigo AMS. 53C21, 53C42.

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