- Text
- Generic,
- Subgroup,
- Fundamental,
- Element,
- Proposition,
- Generated,
- Homomorphism,
- Finite,
- Quotient,
- Projection,
- Galois,
- Closures,
- Projections

On Fundamental Groups of Galois Closures of Generic Projections

**On** **Fundamental** **Groups****of****Galois** **Closures****of****Generic** **Projections**Dissertationzur Erlangungdes Doktorgrades (Dr. rer. nat.)der Mathematisch-Naturwissenschaftlichen Fakultätder Rheinischen Friedrich-Wilhelms-Universität Bonnvorgelegt vonChristian Liedtkeaus GöttingenBonn 2004

- Page 3: Angefertigt mit der Genehmigung der
- Page 6 and 7: 6 Conclusion 636.1 The algorithm of
- Page 8 and 9: to look at the affine situation fir
- Page 10 and 11: 4 We describe a certain quotient of
- Page 12 and 13: The quotations at the beginning of
- Page 14 and 15: We recall that a surface S is calle
- Page 16 and 17: than 2. Knowing B and the homomorph
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- Page 20 and 21: For a proof we refer to [Fa, Sectio
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- Page 24 and 25: Lemma 3.1 Let S be a subgroup of S
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- Page 38 and 39: We let Y be a connected and finite
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- Page 42 and 43: No matter whether we are in the aff
- Page 44 and 45: We already said in Section 4.1 that
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obtain the following two short exac

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If τ 1 and τ 2 have exactly one i

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5.2 The connection with E( − ,n)B

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Remark 5.4 The really hard part of

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So we obtain the following commutat

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For the definition of ϑ(t a ) we h

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with f i ∈ F d and s i ∈ N. Usi

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quotient does not depend on the cho

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PROOF. We have seen the above short

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Examples 5.21 The following H 2 ’

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5.6 Examples from the theory of Cox

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Under the isomorphism given in the

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the compositionδ := Γ 1 · ... ·

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outside a small disc containing the

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taking the quotient of (∗) by C a

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with s(ψ(γ)) we may assume that

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For both groups π top1 (¢ 2 − D

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where ¯δ ′ denotes the image of

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H 2 (X, ¡ ) is an injection. The l

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We look at the projection f n : X n

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7 Examples7.1 2Let X :=2 be the com

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Remark 7.7 Using the results of Moi

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Moishezon and Teicher [MoTe2, Propo

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References[ADKY][BHPV][Bea]D. Aurou

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[MoTe3][MoTe4]B. Moishezon, M. Teic