Conformal automorphisms of algebraic surfaces and algebraic curves in the complex projective space

Abstract

We study the automorphism group of curves and surfaces in CP3 with respect to the conformal group, i.e. the group of all A∈PGL(4,ℂ) commuting with the anti-holomorphic involution j defined by j((z0:z1:z2:z3))=(−z¯1:z¯0:z¯3:−z¯2). For some singular surfaces we check when this group is finite. Among the singular surfaces we handle there are:(1) certain cones;(2) surfaces X containing no line and with j(X)≠X;(3) surfaces containing only finitely many, k, twistor lines with k≥3.In many cases the proofs need results on conformal automorphisms of singular curves.