The bicanonical map of surfaces with $p_g=0$ and $K^2 \geq 7$

dc.creatorLopes, M. Mendes
dc.creatorPardini, R.
dc.date1999-10-14
dc.date2000-09-18
dc.date.accessioned2026-07-07T05:31:10Z
dc.date.available2026-07-07T05:31:10Z
dc.descriptionA minimal surface of general type with $p_g(S)=0$ satisfies $1\le K^2\le 9$ and it is known that the image of the bicanonical map $\fie$ is a surface for $K_S^2\geq 2$, whilst for $K^2_S\geq 5$, the bicanonical map is always a morphism. In this paper it is shown that $\fie$ is birational if $K_S^2=9$ and that the degree of $\fie$ is at most 2 if $K_S^2=7$ or $K_S^2=8$. By presenting two examples of surfaces $S$ with $K_S^2=7$ and 8 and bicanonical map of degree 2, it is also shown that this result is sharp. The example with $K_S^2=8$ is, to our knowledge, a new example of a surface of general type with $p_g=0$.
dc.descriptionLaTeX 2e, 15 pages, to appear. Minor typos, change of title (title of the previous version: "A note on surfaces of general type with $p_g=0$ and $K^2\ge 7$") and added one example of a surface, showing that the main result is sharp
dc.identifierhttps://arxiv.org/abs/math/9910074
dc.identifierhttp://arxiv.org/abs/math/9910074
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79242
dc.subjectAlgebraic Geometry
dc.titleThe bicanonical map of surfaces with $p_g=0$ and $K^2 \geq 7$
dc.typetext

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