Halves of a real Enriques surface

Alexander Degtyarev, Viatcheslav Kharlamov
1996 Commentarii Mathematici Helvetici  
The real part E~ of a real Enriques surface E admits a natural decomposition in two halves, E R = E~)wE~ 2), each half being a union of components of E~. We classify the triads (E~; E~ ~), E~ 2)) up to homeomorphism. Most results extend to surfaces of more general nature than Enriques surfaces. We use and study in details the properties of Kalinin's filtration in the homology of the fixed point set of an involution, which is a convenient tool not widely known in topology of real algebraic
more » ... eal algebraic varieties. 9 br and fir stand for the Betti numbers with the integral and Z/2-coefficients respectively: br(') = rk Hr(' ; 7/) and fir(') = dim Hr(-); 9 /3, is the total Betti number:/3,(.) = Zr>_0 fir('); 9 x(X) is the Euler characteristic of a topological space X; 9 ~(M) is the signature of an oriented manifold M; 9 Torsz G is the 2-primary component of an abelian group G. Generalized Enriques surfaces A nonsingular compact complex surface X will be called a generalized K3-surface if Hi (X; Z/2) = 0 and w2(X) = 0. A generalized Enriques surface is a complex
doi:10.1007/bf02566440 fatcat:m7fbbz2ojnfn7duzxjfadcizxy