Division algebras that ramify only on a plane quartic curve
  Let k be an algebraically closed field of characteristic 0. We prove that any division algebra over k(x,y) whose ramification locus lies on a quartic curve is cyclic. 
Boris E. Kunyavskii, Louis H. Rowen, Sergey V. Tikhonov, and   Vyacheslav I. Yanchevskii