Fundamental group of some genus-2 fibrations and applications (Q2909477)
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scientific article; zbMATH DE number 6074257
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fundamental group of some genus-2 fibrations and applications |
scientific article; zbMATH DE number 6074257 |
Statements
30 August 2012
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Genus-2 fibration
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fundamental group
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holomorphic convexity
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Fundamental group of some genus-2 fibrations and applications (English)
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The paper under review deals with relatively minimal genus-2 fibration \(f:X\longrightarrow C\) where \(X\) is a smooth projective surface and \(C\) is a smooth projective curve. In particular the authors compute the fundamental group \(\pi_1(X)\), analyzing the singular fibres and using the short exact sequence NEWLINE\[NEWLINE \pi_1(F)\rightarrow \pi_1(X)\rightarrow\pi_1(C)\rightarrow (1). NEWLINE\]NEWLINE The result is also used to verify Shafarevic's conjecture when \(b_1(X)>b_1(C)\).
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