Projective normality for some families of surfaces of general type
Issue Date
2017-08-31Author
Rajaguru, Biswajit
Publisher
University of Kansas
Format
55 pages
Type
Dissertation
Degree Level
Ph.D.
Discipline
Mathematics
Rights
Copyright held by the author.
Metadata
Show full item recordAbstract
In this thesis, we present the author's joint research with Lei Song, published in \cite{RS}. We show this: Suppose X is a minimal surface, which is a ramified double covering f:X- S, of a rational surface S, with dim |-K_S|= 1. And suppose L is a divisor on S, such that L.L= 7 and L. C= 3 for any curve C on S. Then K_X+f*L is base-point free and the natural map Sym^r(H^0(K_X+f*L))- H^0(r(K_X+f*L)), is surjective for all r=1. In particular this implies, when S is also smooth and L is an ample line bundle on S, that K_X+nf*L embeds X as a projectively normal variety for all n = 3.
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