Corrections to “Algebraic relations among extremal lengths of homology classes on compact Riemann surfaces”

✍ Scribed by Makoto Masumoto

• Publisher: John Wiley and Sons
• Year: 2003
• Tongue: English
• Weight: 52 KB
• Volume: 248-249
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200310017

✦ Synopsis

In [1], given a canonical decomposition H 1 (R) = G 1 +G 2 of the homology group of a compact Riemann surface R of genus 2, we have investigated the set ∆[G 1 , G 2 ] of the diagonal entries of period matrices associated with the decomposition. Theorem 1.

the same hyperbolic radius, where Γ = P SL(2, Z). However, this is false. We have proved only that the closure of p j (∆[G 1 , G 2 ]) in H is identical with ΓC j for j = 1, 2, where p j : H × H → H denotes the projection onto the j-th component: p j (τ 1 , τ 2 ) = τ j . Since C 1 and C 2 have the same hyperbolic radius, the modified theorem still shows a new symmetry of compact Riemann surfaces of genus two.