Moduli space of connections on a irregular rational curve

Abstract: We study the compactification of the moduli space of a certain class of rank-two irregular connections on the Riemann sphere, presenting one double pole and two simple poles. To explicitely build the compactification, we identify a class of irregular connections with an irregular rational curve and an extra complex parameter. As a first step, we will inspire to the Deligne and Mumford's work to compactify the moduli space of such irregular rational curves, introducing the notion of irregular stable nodal curve. Secondly, we will understand the behaviour of the extra complex parameter to conclude the compactification.