Abstract:
In this article we construct all kinds of elementary Prym differentials for arbitrary characters on a variable torus with a finite numbers of punctures and find the dimensions of two important quotient spaces. As a consequence, this yields the dimension of the first holomorphic de Rham cohomology group of Prym differentials for arbitrary characters on torus. Also, we construct explicit bases in these quotient spaces.
Keywords:Prym differentials for arbitrary characters, the Gunning cohomological bundle over the Teichmuller space torus with a finite numbers of punctures.
UDC:515.17+517.545
Received: 12.01.2014 Received in revised form: 24.02.2014 Accepted: 30.03.2014