Celal Cem Sarıoğlu (DEÜ)

December 14, Time:10:15, Place: B259

**Abstract:** From the Geometry-Topology courses everyone knows the number of holes of an orientable compacts surface is known as a genus,and it is related with its Euler characteristic. On the other hand, in algebraic geometry, there are two related definitions of genus of an irreducible projective algebraic curve C: the arithmetic genus, and the geometric genus. If the curve C has no singular points these two concepts will coincide and also coincide with the topological definition applied to Riemann surfaces of C. In this talk, we will introduce how can we compute the arithmetic and geometric genus of an irreducible projective algebraic curve and how they are related to the genus of an oriented Riemann surface.