We give an algebraic construction of the moduli space of irregular singular connections of generic ramified type on a smooth projective curve. We prove that the moduli space is smooth and give its dimension. Under the assumption that the exponent of ramified type is generic, we give an algebraic symplectic form on the moduli space. Introduction Moduli space of irregular singular connections are...

In this article we consider the moduli space of smooth n-pointed nonhyperelliptic curves of genus three. In the pursuit of cohomological information about this space, we make Sn-equivariant counts of its numbers of points defined over finite fields for n up to seven. Together with results on the moduli spaces of smooth pointed curves of genus zero, one and two, and the moduli space of smooth hy...