On surfaces with pg = 2, q = 1 and non-birational bicanonical map

2002 ◽  
pp. 117-126
Keyword(s):  
Bicanonical Map

THE BICANONICAL MAP OF SURFACES WITH $p_g = 0$ AND $K^2 \geqslant 7$, II

2003 ◽  
Vol 35 (03) ◽  
pp. 337-343 ◽  
Author(s):  
MARGARIDA MENDES LOPES ◽  
RITA PARDINI
Keyword(s):  
Bicanonical Map

scholarly journals THE BICANONICAL MAP OF SURFACES WITH pg = 0 AND K2 [ges ] 7

2001 ◽  
Vol 33 (3) ◽  
pp. 265-274 ◽  
Author(s):  
MARGARIDA MENDES LOPES ◽  
RITA PARDINI
Keyword(s):  
Minimal Surface ◽  
General Type ◽  
Surfaces Of General Type ◽  
Bicanonical Map ◽  
Surface Of General Type

A minimal surface of general type with pg(S) = 0 satisfies 1 [les ] K2 [les ] 9, and it is known that the image of the bicanonical map φ is a surface for K2S [ges ] 2, whilst for K2S [ges ] 5, the bicanonical map is always a morphism. In this paper it is shown that φ is birational if K2S = 9, and that the degree of φ is at most 2 if K2S = 7 or K2S = 8.By presenting two examples of surfaces S with K2S = 7 and 8 and bicanonical map of degree 2, it is also shown that this result is sharp. The example with K2S = 8 is, to our knowledge, a new example of a surface of general type with pg = 0.The degree of φ is also calculated for two other known surfaces of general type with pg = 0 and K2S = 8. In both cases, the bicanonical map turns out to be birational.

Remarks on the bicanonical map for surfaces of general type

1997 ◽  
Vol 224 (1) ◽  
pp. 137-166 ◽  
Author(s):  
Ciro Ciliberto ◽  
Paolo Francia ◽  
Margarida Mendes Lopes
Keyword(s):  
General Type ◽  
Surfaces Of General Type ◽  
Bicanonical Map

On the Birationality of the Bicanonical Map of a Surface Section of a Threefold

2007 ◽  
Vol 35 (5) ◽  
pp. 1627-1650
Author(s):  
M. C. Beltrametti ◽  
C. Ciliberto ◽  
A. Lanteri ◽  
A. J. Sommese
Keyword(s):  
Bicanonical Map ◽  
Surface Section

scholarly journals Some bidouble planes with pg = q = 0 and 4 ≤ K2 ≤ 7

2015 ◽  
Vol 26 (05) ◽  
pp. 1550035 ◽  
Author(s):  
Carlos Rito
Keyword(s):  
General Type ◽  
Enriques Surface ◽  
Surfaces Of General Type ◽  
Bicanonical Map ◽  
Double Coverings

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 K2 = 4, …, 7 are constructed as double coverings of an Enriques surface. These surfaces have a description as bidouble coverings of the plane.

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