The cohomology solution and the index theorem on ring surfaces of genus g
Changfeng Xue Yancheng Institute of Technology, Yancheng, Jiangsu 224003, P.R. China
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.
