Riemann surfaces and restrictively-marked hypermaps

作者：d'Azevedo Antonio Breda^*

来源：Ars Mathematica Contemporanea, 2010, 3(1): 87-98.

• Groups
• Riemann surface
• hypermaps
• maps
• restrictedly-marked
• restrictedly regular

If S is a compact Riemann surface of genus g > 1, then S has at most 84(g - 1) (orientation preserving) automorphisms (Hurwitz). On the other hand, if G is a group of automorphisms of S and vertical bar G vertical bar > 24(g - 1) then G is the automorphism group of a regular oriented map (of genus g) and if vertical bar G vertical bar > 12(g 1) then G is the automorphism group of a regular oriented hypermap of genus g (Singerman). We generalise these results and prove that if vertical bar G vertical bar > g 1 then G is the automorphism group of a regular restrictedly-marked hypermap of genus g. As a special case we also show that a marked finite transitive permutation group (Singerman) is a restrictedly-marked hypermap with the same genus.

• 出版日期2010