The goal of this note is to prove that the mapping class groups of closed orientable surfaces of genus 2 (with punctures) are not KÃ¤hler. An application to compactifications of the moduli space ofâ€¦ (More)

All varieties are defined over C and projective. A well-known result of Hurwitz states that the maximal order of the automorphism group of a smooth curve of genus g is 42(2gâˆ’2). This bound is notâ€¦ (More)

Throughout this article we assume n > 2 and Ç« = 0. All varieties are defined over an algebraically closed field k. In [HMP98], Harris, Mazur, and Pandharipande ask: given a smooth, degree dâ€¦ (More)

We prove a sharp bound for the automorphism group of a stable curve of a given genus and describe all curves attaining that bound. All curves are defined over C and projective. A well-known result ofâ€¦ (More)

Let G be a connected simple cubic graph; Aut G denotes its automorphism group. Let n be half the number of vertices of G. We define the arithmetic genus of a (possibly disconnected) graph as eâˆ’v+1â€¦ (More)