Surfaces with $$p_g = q= 1$$ p g = q = 1 , $$K^2 = 7$$ K 2 = 7 and non-birational bicanonical maps
نویسندگان
چکیده
منابع مشابه
On Surfaces with P G = 2, Q = 1 and Non-birational Bicanonical Map *
In the present note we show that any surface of general type over C with pg = 2,q = 1 and non birational bicanonical map has a pencil of curves of genus 2. Combining this result with previous ones, one obtains that an irregular surface S of general type with χ(S) ≥ 2 and non-birational bicanonical map has a pencil of curves of genus 2.
متن کاملOn Surfaces with P G = Q = 2 and Non-birational Bicanonical Map *
The present paper is devoted to the classification of irregular surfaces of general type with pg = q = 2 and non birational bicanonical map. The main result is that, if S is such a surface and if S is minimal with no pencil of curves of genus 2, then S is a double cover of a principally polarized abelian surface (A,Θ), with Θ irreducible. The double cover S → A is branched along a divisor B ∈ |...
متن کاملM ar 2 00 7 On surfaces with p g = q = 1 and non - ruled bicanonical involution
This paper classifies surfaces of general type S with pg = q = 1 having an involution i such that S/i has non-negative Kodaira dimension and that the bicanonical map of S factors through the double cover induced by i. It is shown that S/i is regular and either: a) the Albanese fibration of S is of genus 2 or b) S has no genus 2 fibration and S/i is birational to a K3 surface. For case a) a list...
متن کامل5 On surfaces with p g = q = 1 and non - ruled bicanonical involution
We classify surfaces of general type S with pg = q = 1 having an involution i such that S/i is non-ruled and the bicanonical map of S factors through the natural cover S → S/i. We prove that the minimal model of S/i is either a K3 surface or a surface of Kodaira dimension 1 (in this last case S has a genus 2 fibration). We also show that these cases do occur. In particular we construct a surfac...
متن کاملm at h . A G ] 1 3 N ov 2 00 1 THE BICANONICAL MAP OF SURFACES WITH p g = 0 AND K 2 ≥ 7 , II
We study the minimal complex surfaces of general type with pg = 0 and K 2 = 7 or 8 whose bicanonical map is not birational. We show that if S is such a surface, then the bicanonical map has degree 2 (see [MP1]) and there is a fibration f : S → P such that: i) the general fibre F of f is a genus 3 hyperelliptic curve; ii) the involution induced by the bicanonical map of S restricts to the hypere...
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ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2014
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-014-9990-2