Bonner Mathematische Schriften. Vol.390: Teichmüller curves in the Deligne-Mumford compactification: Diss. … Dr. rer. nat. / Ronkin I. - Bonn: Rheinische Friedrich - Wilhelms - Universität, 2009. - 42 p. - ref.: p.41-42. - ISSN 0524-045X  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Contents

0 Introduction ................................................. 1 1 Moduli spaces as orbifolds ................................... 3 1.1 Orbifolds ............................................... 4 1.2 Moduli spaces ........................................... 6 2 Flat and translation surfaces ............................... 11 3 Teichmüller discs and curves ................................ 14 3.1 Teichmüller discs ...................................... 14 3.2 Properties of Teichmüller discs ........................ 16 3.3 Teichmüller curves ..................................... 18 3.4 Abelian Teichmüller curves ............................. 20 3.5 Examples ............................................... 20 4 Cusps of Teichmüller curves ................................. 24 5 Universal curve over a cusp ................................. 26 5.1 Surface bundle over a disc ............................. 26 5.2 The fibers of the surface bundle ....................... 28 5.3 Intersection with the compactification divisor ......... 30 5.4 Examples ............................................... 32 6 Evaluation of K1 on abelian Teichmüller curves .............. 35 6.1 Holomorphic section in β and its zeros ................. 35 6.2 Holomorphic section in the cotangent bundle of the universal curve .................................... 36 6.3 Evaluation of к1 on V and on С ......................... 37 6.4 Weil-Petersson vs. Teichmüller area .................... 39 6.5 Examples ............................................... 40