Some bidouble planes with p_g= q = 0 and 4 ≤ K²≤ 7

Abstract

We give a list of possibilities for surfaces of general type with pg = 0 having an involution i such that the bicanonical map of S is not composed with i and S/i is not rational. Some examples with K 2 = 4, . . . , 7 are constructed as double coverings of an Enriques surface. These surfaces have a description as bidouble coverings of the plane.

A new family of surfaces of general type with $$K^2=7$$ K 2 = 7 and $$p_g=0$$ p g = 0

“…Finally, as a comparison to Proposition 5.1 and Remark 5.1, we remark that T 2 is birational to an Enriques surface as described in [Ri12], and it realizes the case k = 9, K 2 W = −2 and B 0 = Γ 0 (3,0) + Γ 1 (1,−2) in the list of [LS12].…”

“…We show that three quotients of S by the involutions have respectively Kodaira dimensions −∞, 0, 1, realizing some numerical possibilities of the lists of [Ri12] and [LS12]. By applying the results of a recent article [Bau12], we prove that S satisfies Bloch's conjecture.…”

“…We will point out that one of the quotient is birational to an Enriques surface. In [Ri12], a family of surfaces of general type with K 2 = 7 is constructed as bidouble planes. However, here we show that the family with K 2 = 7 in [Ri12] consists of Inoue surfaces.…”

A two-dimensional family of surfaces of general type with $p_g=0$ and $K^2=7$

“…Mendes Lopes and Pardini [18] studied the bicaonical map of a surface S of general type with p g = 0 and K 2 S = 7 and showed that the bicanonical map of an Inoue surface has degree two. Lee and the second named author [17] provided all possible fixed loci of an involution σ on S (see also [20]). Especially, they showed that there only two cases for the divisorial fixed part R σ when the quotient of S by σ is birational to an Enriques surface:…”

Notes on Automorphisms of Surfaces of General Type With And

“…We focus on automorphisms of minimal smooth complex surfaces of general type with and . Involutions on such surfaces have been studied in [16] and [24]. All the possibilities of the quotient surfaces and the fixed loci of the involutions are listed.…”