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On Manin's conjecture for a certain singular cubic surface

✍ Scribed by Régis de la Bretèche; Tim D. Browning; Ulrich Derenthal

Publisher: NUMDAM (Numrisation de Documents Anciens Mathmatiques)
Year: 2007
Tongue: French
Weight: 471 KB
Volume: 40
Category: Article
ISSN: 0012-9593
DOI: 10.1016/j.ansens.2006.12.002

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Problem 142. : The symmetric genus of a

Problem 142. : The symmetric genus of a group G is the minimum genus of a surface on which G acts. Let An denote the alternating group of degree n, γG denote the genus of the group G, and σ(G) the symmetric genus of G. Is the following conjecture true? Conjecture: For at least one n, γ(An)<σ(An)?

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## Reseirrch problems Problem 142. The symmetric genus of a group G is the minimum genus of a surface on which G acts. Let A, denote the alternating group of degree n, y(G) denote the genus of the group G, and a(G) the symmetric genus of G. Is the following conjecture true? Conjecture: For at leas