A Fake Projective Plane with an Order 7 Automorphism
نویسندگان
چکیده
A fake projective plane is a compact complex surface (a compact complex manifold of dimension 2) with the same Betti numbers as the complex projective plane, but not isomorphic to the complex projective plane. As was shown by Mumford, there exists at least one such surface. In this paper we prove the existence of a fake projective plane which is birational to a cyclic cover of degree 7 of a Dolgachev surface.
منابع مشابه
Cyclic Quotients of Fake Projective Planes
Recently, Prasad and Yeung classified all possible fundamental groups of fake projective planes. According to their result, many fake projective planes admit an automorphism of prime order, and in that case the order must be 3 or 7. Let σ be an automorphism of prime order of a fake projective plane X. In this paper we classify all possible structures of the quotient surface X/σ and its minimal ...
متن کاملQuotients of Fake Projective Planes
Recently, Prasad and Yeung classified all possible fundamental groups of fake projective planes. According to their result, many fake projective planes admit a nontrivial group of automorphisms, and in that case it is isomorphic to Z/3Z, Z/7Z, 7 : 3, or (Z/3Z), where 7 : 3 is the unique non-abelian group of order 21. Let G be a group of automorphisms of a fake projective plane X. In this paper ...
متن کاملExceptional Collection of Objects on Some Fake Projective Planes
The purpose of the article is to explain a new method to study existence of a sequence of exceptional collection of length three for fake projective planes M with large automorphism group. This provides more examples to a question in [GKMS].
متن کاملFake Projective Planes
1.1. A fake projective plane is a smooth compact complex surface which is not the complex projective plane but has the same Betti numbers as the complex projective plane. Such a surface is known to be projective algebraic and it is the quotient of the (open) unit ball B in C (B is the symmetric space of PU(2, 1)) by a torsion-free cocompact discrete subgroup of PU(2, 1) whose Euler-Poincaré cha...
متن کاملLine-transitive Automorphism Groups of Linear Spaces
In this paper we prove the following theorem. Let S be a linear space. Assume that S has an automorphism group G which is line-transitive and point-imprimitive with k < 9. Then S is one of the following:(a) A projective plane of order 4 or 7, (a) One of 2 linear spaces with v = 91 and k = 6, (b) One of 467 linear spaces with v = 729 and k = 8. In all cases the full automorphism group Aut(S) is ...
متن کامل