The fundamental group of a quotient of a product of curves

Dedieu, Thomas; Perroni, Fabio

doi:10.1515/jgt.2011.104

Cited by 8 publications

(8 citation statements)

References 12 publications

(21 reference statements)

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“…In this section we prove that X n and Y n have finite fundamental group. In order to do this we apply the main theorem of [Arm68] in the case of product quotient varieties following [BCGP12,DP12]. We briefly recall their strategy and we refer to them for further details.…”

Section: The Fundamental Groupmentioning

confidence: 99%

Rigid Manifolds of general type with non-contractible universal cover

Frapporti¹,

Gleissner²

2021

Preprint

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Section: The Fundamental Groupmentioning

confidence: 99%

Rigid Manifolds of general type with non-contractible universal cover

Frapporti¹,

Gleissner²

2021

Preprint

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“…This topic is treated in greater generality in [DP12] and we refer to it for further details. = a 1 , b 1 , .…”

Section: Group Theoretical Description and Invariants Of Threefolds Imentioning

confidence: 99%

On threefolds isogenous to a product of curves

Frapporti

Gleissner

2016

Journal of Algebra

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Abstract.A threefold isogenous to a product of curves X is a quotient of a product of three compact Riemann surfaces of genus at least two by the free action of a finite group. In this paper we study these threefolds under the assumption that the group acts diagonally on the product. We show that the classification of these threefolds is a finite problem, present an algorithm to classify them for a fixed value of χ(O X ) and explain a method to determine their Hodge numbers. Running an implementation of the algorithm we achieve the full classification of threefolds isogenous to a product of curves with χ(O X ) = −1, under the assumption that the group acts faithfully on each factor.

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“…Thus this case cannot occur. Finally we have to consider Example 2.9 from [29] from which we get F * (X) = SL 2 (17) but in this last case the large prime divisor is comes from q 8 − 1 and not q 6 − 1 and so this case is also impossible. Thus we infer that G = X.…”

Section: Exceptional Groupsmentioning

confidence: 99%

“…We have that {e, f } ⊂ {4, 6, 10, 12, 18} by Theorem 2.2. Consideration of these possibilities yield the examples in rows ( 6) to (17). Note that the case that e = 4 and d = 6 falls as Alt (7) has no elements of order 9.…”

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confidence: 99%

Generation of finite quasisimple groups with an application to groups acting on Beauville surfaces

Fairbairn

Magaard

Parker

2013

Proceedings of the London Mathematical Society

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We develop theorems which produce a multitude of hyperbolic triples for the finite classical groups. We apply these theorems to prove that every quasisimple group except Alt (5) and SL 2(5) is a Beauville group. In particular, we settle a conjecture of Bauer, Catanese and Grunewald which asserts that all non‐abelian finite quasisimple groups except for the alternating group Alt (5) are Beauville groups.

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The fundamental group of a quotient of a product of curves

Abstract: Abstract. We prove a structure theorem for the fundamental group of the quotient X of a product of curves by the action of a finite group G and, hence, for that of any resolution of the singularities of X.

Cited by 8 publications

References 12 publications

Rigid Manifolds of general type with non-contractible universal cover

Rigid Manifolds of general type with non-contractible universal cover

On threefolds isogenous to a product of curves

Generation of finite quasisimple groups with an application to groups acting on Beauville surfaces

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