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Enumeration of the 50 fake projective planes = Énumération des 50 faux plans projectifs

Cartwright, Donald I. and Steger, Tim Joshua (2010) Enumeration of the 50 fake projective planes = Énumération des 50 faux plans projectifs. Comptes rendus. Mathematique, Vol. 348 (1-2), p. 11-13. ISSN 1631-073X. Article.

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DOI: 10.1016/j.crma.2009.11.016

Abstract

Building upon the classification of Prasad and Yeung [Invent. Math. 168 (2007) 321–370], we have shown that there exist exactly 50 fake projective planes (up to homeomorphism; 100 up to biholomorphism), and exhibited each of them explicitly as a quotient of the unit ball in C2. Some of these fake planes admit singular quotients by 3 element groups and three of these quotients are simply connected. Also exhibited are algebraic surfaces with c21=3c2=9n for any positive integer n.

En partant de la classification de Prasad et Yeung [Invent. Math. 168 (2007) 321–370], nous montrons qu'il existe précisément 50 faux plans projectifs (à homéomorphisme près, 100 à biholomorphisme près), et présentons chacun comme un quotient de la boule unité de C2. Certains de ces plans admettent des quotients singuliers par des groupes d'automorphismes à 3 éléments, et trois d'entre eux sont simplement connexes. De plus, pour chaque entier n>0, nous présentons des surfaces algébriques avec c21=3c2=9n.

Item Type:Article
ID Code:5684
Status:Published
Refereed:Yes
Uncontrolled Keywords:Homeomorphism, biholomorphism, algebraic surface,
homéomorphisme, biholomorphisme, surface algébrique
Subjects:Area 01 - Scienze matematiche e informatiche > MAT/05 Analisi matematica
Divisions:001 Università di Sassari > 03 Istituti > Matematica e fisica
Publisher:Elsevier
ISSN:1631-073X
Copyright Holders:© 2009 Académie des sciences Published by Elsevier Masson
Additional Information:Article presented by Pierre Deligne
Deposited On:08 Mar 2011 09:59

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