Period determinant of an irregular connection over an elliptic curve

Abstract

In this article, we calculate the period determinant of an irrgular singular connection d+dy on the legendre curve U: y^2 =x(x-1)(x- lambda). We calculate its de Rham cohomology and the cycles in the homology of the dual connection and describe the period matrix. Terasoma's work is introduced to approximate the direct image connection pi_*(\nabla) by a sequence of regular connections as an intermediate step where pi:U -> A^1(y), (x,y) |-> y. Finally, we will compare the period obtained by this approximation of the direct image connection and the original.