07-23【宋基建】物质楼C1124 GAP研讨班系列讲座之207

发布者:卢珊珊发布时间:2021-07-19浏览次数:10


TitleIrreducible cone spherical metrics and stable extensions of two line bundles

Speaker宋基建 (天津大学应用数学中心) 

Time2021723日,周五,上午  10:00-11:30 

Room:科大东区 物质科研楼C1124

 

AbstractCone spherical metrics on compact Riemann surfaces are conformal metrics of constant curvature +1 with finitely many conical singularities. They are called irreducible if any developing maps of such metrics don't have monodromy in U(1). By using projective structures and indigenous bundles on compact Riemann surfaces, we construct a canonical surjective map from the moduli space of stable extensions of two line bundles to that of irreducible cone spherical metrics with cone angles in 2πZ. We also prove that the map is generically injective in algebro-geometric sense if the Riemann surface has genus ≥2. As an application, we obtain some new existence results about irreducible cone spherical metrics. This is a joint work with Lingguang Li and Bin Xu.