65 research outputs found
On the birationality of the adjunction mapping of projective varieties
Let be a smooth projective -fold such that and a globally
generated, big line bundle on such that . We give
necessary and sufficient conditions for the adjoint systems to be
birational for . In particular, for Calabi-Yau -folds we
generalize and prove parts of a conjecture of Gallego and Purnaprajna.Comment: 7 pages, accepted for publication in Journal of the Ramanujan
Mathematical Societ
Remarks on families of singular curves with hyperelliptic normalizations
We give restrictions on the existence of families of curves on smooth
projective surfaces of nonnegative Kodaira dimension all having constant
geometric genus and hyperelliptic normalizations. In particular, we
prove a Reider-like result whose proof is ``vector bundle-free'' and relies on
deformation theory and bending-and-breaking of rational curves in \Sym^2(S).
We also give examples of families of such curves.Comment: 18 page
Smooth curves on projective K3 surfaces
In this paper we give for all , d>0, necessary and
sufficient conditions for the existence of a pair (X,C), where X is a K3
surface of degree 2n in \matbf{P}^{n+1} and C is a smooth (reduced and
irreducible) curve of degree d and genus g on X. The surfaces constructed have
Picard group of minimal rank possible (being either 1 or 2), and in each case
we specify a set of generators. For we also determine when X can be
chosen to be an intersection of quadrics (in all other cases X has to be an
intersection of both quadrics and cubics). Finally, we give necessary and
sufficient conditions for \O_C (k) to be non-special, for any integer .Comment: 12 pages, to appear in Math. Scand. Mistake in earlier version of Thm
1.1 corrected and its proof is considerably simplified (removed the now
redundant Sections 4 and 5 of the previous version). Added Rem. 1.2 and Prop.
1.
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