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Let $f:S\to S$ be a given periodic map of order $n$, and $(m_i,\lambda_i, \sigma_i)$ be the valency of the multiple point $p_i$ of $f$ ( $i=1,\cdots,r$ ).

A classical result says such $f$ is isotopic to a product of Dehn twists. It is trivial when $n=1$. Now we assume that $n>1$. I want to know how to get such a Dehn twist presentation.

For a pseudo-periodic map, a similar Dehn twist presentation implies Picard-Lefschetz formula of the monodromy of a singular fiber (semistable or non-semistable). In fact, I wish to comupte the monodromy of a non-semistable fiber.

For hyperelliptic periodic maps, Ishzaka provided a method.

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    $\begingroup$ How is the map given in the first place? $\endgroup$
    – Igor Rivin
    Commented Jan 1, 2011 at 2:48
  • $\begingroup$ The above question is answered in some detail by my answer to the following: mathoverflow.net/questions/142365/… $\endgroup$
    – Sam Nead
    Commented Jan 13, 2014 at 21:38
  • $\begingroup$ So, I am voting to close. $\endgroup$
    – Sam Nead
    Commented Jan 13, 2014 at 21:40
  • $\begingroup$ @SamNead: Do you think it is reasonable to close an old question as a duplicate of a much newer question? $\endgroup$
    – Stefan Kohl ♦
    Commented Jan 13, 2014 at 23:44
  • $\begingroup$ @Stefan: Well, the alternative is to cut-and-paste my answer. But I thought that would be poor form. $\endgroup$
    – Sam Nead
    Commented Jan 15, 2014 at 22:28

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