Generic covers branched over {xn=ym}

✍ Scribed by Sandro Manfredini; Roberto Pignatelli

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 295 KB
• Volume: 103
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(98)00160-6

✦ Synopsis

In this paper the authors study generic covers of C 2 branched over {x n + y m } = 0 s.t. the total space is a normal analytic surface.

They found a complete description of the monodromy of the cover in terms of the monodromy graphs and an almost complete description of the local fundamental groups in case (n, m) = 1.

For the general case, they give explicit descriptions of base changes in terms of monodromy graphs; they describe completely the embedded resolution graphs in the case n|m. Via these base changes every cover is a quotient of such a cover.