560 research outputs found
Estimates of the number of rational mappings from a fixed variety to varieties of general type
First we find effective bounds for the number of dominant rational maps between two fixed smooth projective varieties with ample
canonical bundles. The bounds are of the type , where , is the canonical bundle of and
are some constants, depending only on . Then we show that for any variety
there exist numbers and with the following properties: For
any threefold of general type the number of dominant rational maps is bounded above by . The number of threefolds , modulo birational
equivalence, for which there exist dominant rational maps , is
bounded above by . If, moreover, is a threefold of general type, we
prove that and only depend on the index of the
canonical model of and on .Comment: A revised version. The presentation of results and proofs has been
improved. AMS-TeX, 19 page
On C-fibrations over projective curves
The goal of this paper is to present a modified version (GML) of ML invariant
which should take into account rulings over a projective base and allow further
stratification of smooth affine rational surfaces. We provide a non-trivial
example where GML invariant is computed for a smooth affine rational surface
admitting no C-actions. We apply GML invariant to computation of ML invariant
of some threefolds.Comment: 21 pages, LaTe
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