On equations of fake projective planes with automorphism group of order $21$

Lev Borisov

Type: Article

Publication Date: 2023-05-30

Citations: 0

DOI: https://doi.org/10.46298/epiga.2023.8507

Abstract

We study Dolgachev elliptic surfaces with a double and a triple fiber and find explicit equations of two new pairs of fake projective plane with $21$ automorphisms, thus finishing the task of finding explicit equations of fake projective planes with this automorphism group. This includes, in particular, the fake projective plane discovered by J. Keum. Comment: 19 pages + supplemental files

Locations

Épijournal de Géométrie Algébrique - View - PDF
arXiv (Cornell University) - View - PDF

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Works That Cite This (0)

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Works Cited by This (13)

Action	Title	Year	Authors
+	The Magma Algebra System I: The User Language	1997	Wieb Bosma John Cannon Catherine Playoust
+	A fake projective plane with an order 7 automorphism	2006	JongHae Keum
+ PDF Chat	Enumeration of the 50 fake projective planes	2009	Donald I. Cartwright Tim Steger
+ PDF Chat	An elliptic surface covered by Mumford's fake projective plane	1988	Masa-Nori Ishida
+ PDF Chat	An Algebraic Surface with K Ample, (K 2 ) = 9, p g = q = 0	1979	D. Mumford
+ PDF Chat	On real structures on rigid surfaces	2002	Вик. С. Куликов Viatcheslav Kharlamov
+ PDF Chat	A fake projective plane via 2-adic uniformization with torsion	2017	Daniel Allcock Fumiharu Kato
+ PDF Chat	Explicit equations of a fake projective plane	2020	Lev Borisov JongHae Keum
+	New explicit constructions of surfaces of general type	2020	Lev Borisov Enrico Fatighenti
+ PDF Chat	Fake projective planes	2007	Gopal Prasad Sai-Kee Yeung