ar X iv : m at h / 01 07 14 2 v 1 [ m at h . A G ] 1 9 Ju l 2 00 1 Elliptic subfields and automorphisms of genus 2 function fields

ar X iv : m at h / 03 07 23 0 v 1 [ m at h . A G ] 1 6 Ju l 2 00 3 EXPLICIT EQUATIONS OF SOME ELLIPTIC MODULAR SURFACES

We present explicit equations of semi-stable elliptic surfaces (i.e., having only type In singular fibers) which are associated to the torsion-free genus zero congruence subgroups of the modular group as classified by A. Sebbar.

ar X iv : m at h / 04 01 05 6 v 1 [ m at h . G T ] 7 J an 2 00 4 SQUARE - TILED SURFACES IN H ( 2 )

This is a study of square-tiled translation surfaces in the stratum H(2) and their SL(2, R)-orbits or Teichmüller discs, which are arithmetic. We prove that for prime n > 3 translation surfaces tiled by n squares fall into two Teichmüller discs, only one of them with elliptic points, and that the genus of these discs has a cubic growth rate in n.

ar X iv : m at h / 03 09 40 8 v 2 [ m at h . D G ] 1 2 Ju l 2 00 4 EINSTEIN METRICS ON SPHERES

ar X iv : 0 70 7 . 40 46 v 1 [ m at h . A G ] 2 7 Ju l 2 00 7 CLIFFORD ’ S THEOREM FOR COHERENT SYSTEMS

Let C be an algebraic curve of genus g ≥ 2. We prove an analogue of Clifford’s theorem for coherent systems on C and some refinements using results of Re and Mercat.

ar X iv : m at h / 02 07 29 6 v 1 [ m at h . M G ] 3 1 Ju l 2 00 2 Products of hyperbolic metric spaces

Let (Xi, di), i = 1, 2, be proper geodesic hyperbolic metric spaces. We give a general construction for a " hyperbolic product " X1× h X2 which is itself a proper geodesic hyperbolic metric space and examine its boundary at infinity.