1. CJM Online first
|Explicit models for threefolds fibred by K3 surfaces of degree two|
We consider threefolds that admit a fibration by K3 surfaces over a nonsingular curve, equipped with a divisorial sheaf that defines a polarisation of degree two on the general fibre. Under certain assumptions on the threefold we show that its relative log canonical model exists and can be explicitly reconstructed from a small set of data determined by the original fibration. Finally we prove a converse to the above statement: under certain assumptions, any such set of data determines a threefold that arises as the relative log canonical model of a threefold admitting a fibration by K3 surfaces of degree two.
Keywords:threefold, fibration, K3 surface
Categories:14J30, 14D06, 14E30, 14J28
2. CJM 1998 (vol 50 pp. 342)
|Shape fibrations, multivalued maps and shape groups |
The notion of shape fibration with the near lifting of near multivalued paths property is studied. The relation of these maps---which agree with shape fibrations having totally disconnected fibers---with Hurewicz fibrations with the unique path lifting property is completely settled. Some results concerning homotopy and shape groups are presented for shape fibrations with the near lifting of near multivalued paths property. It is shown that for this class of shape fibrations the existence of liftings of a fine multivalued map, is equivalent to an algebraic problem relative to the homotopy, shape or strong shape groups associated.
Keywords:Shape fibration, multivalued map, homotopy groups, shape, groups, strong shape groups
Categories:54C56, 55P55, 55Q05, 55Q07, 55R05