2012
DOI: 10.1142/s0129167x12500802
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Fundamental Group of Some Genus-2 Fibrations and Applications

Abstract: We will prove that given a genus-2 fibration f : X → C on a smooth projective surface X such that b1(X) = b1(C) + 2, the fundamental group of X is almost isomorphic to π1(C) × π1(E), where E is an elliptic curve. We will also verify the Shafarevich Conjecture on holomorphic convexity of the universal cover of surfaces X with genus-2 fibration X → C such that b1(X) > b1(C).In the last section we will use the theorem to verify of the Shafarevich Conjecture for genus-2 fibrations such that b 1 (X) > b 1 (C). Coro… Show more

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“…The topic of Shafarevitch conjecture and Shafarevich dimension is discussed in [7], [17]. A different point of view is given by Gurjar and his co-authors (see [14], [15]): they studied some fibrations p : Y → B of compact surfaces and proved that the image of the fundamental group of any fiber in the fundamental group of Y is finite.…”
mentioning
confidence: 99%
“…The topic of Shafarevitch conjecture and Shafarevich dimension is discussed in [7], [17]. A different point of view is given by Gurjar and his co-authors (see [14], [15]): they studied some fibrations p : Y → B of compact surfaces and proved that the image of the fundamental group of any fiber in the fundamental group of Y is finite.…”
mentioning
confidence: 99%