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Projective normality for some families of surfaces of general type
Rajaguru, Biswajit
Rajaguru, Biswajit
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Abstract
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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Date
2017-08-31
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University of Kansas
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This item contains archived web content.
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Keywords
Mathematics, anticanonical rational surfaces, mukai's conjecture, projective normality