%0 Journal Article %T On the rationality of the moduli space of L¨¹roth quartics %A Christian B£¿hning %A Hans-Christian Graf v. Bothmer %J Mathematics %D 2010 %I arXiv %X We prove that the moduli space M_L of L"uroth quartics in P^2, i.e. the space of quartics which can be circumscribed around a complete pentagon of lines modulo the action of PGL_3(CC) is rational, as is the related moduli space of Bateman seven-tuples of points in P^2. %U http://arxiv.org/abs/1003.4635v1