On normal surface singularities and a problem of enriques
作者:
C. Ciliberto,
S. Greco,
期刊:
Communications in Algebra
(Taylor Available online 2000)
卷期:
Volume 28,
issue 12
页码: 5891-5913
ISSN:0092-7872
年代: 2000
DOI:10.1080/00927870008827195
出版商: Gordon and Breach Science Publishers Ltd.
关键词: 14J17;32S05
数据来源: Taylor
摘要:
We construct families of normal surface singularities with the following property: given any fiat projective connected familyV→Bof smooth, irreducible, minimal algebraic surfaces, the general singularity in one of our families cannot occur, analytically, on any algebraic surfaces which is Irrationally equivalent to a surface inV→B. In particular this holds forV→Bconsisting of a single rational surface, thus answering negatively to a long standing problem posed by F. Enriques. In order to prove the above mentioned results, wo develop a general, though elementary, method, based on the consideration of suitable correspondences, for comparing a given family of minimal surfaces with a family of surface singularities. Specifically the method in question gives us the possibility of comparing the parameters on which the two families depend, thus leading to the aforementioned results.
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