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...
In this paper, using techniques of value distribution theory, we give a uniqueness theorem for meromorphic mappings of into with truncated multiplicities and “few" targets. We also give a theorem of linear degeneration for such maps with truncated multiplicities and moving targets.
In 1981 J. Noguchi proved that in a logarithmic algebraic manifold, having logarithmic irregularity strictly bigger than its dimension, any entire curve is algebraically degenerate.
In the present paper we are interested in the case of manifolds having logarithmic irregularity equal to its dimension. We restrict our attention to Brody curves, for which we resolve the problem completely in dimension 2: in a logarithmic surface with logarithmic irregularity and logarithmic...
In this article, we study the ramification of the Gauss map of complete minimal surfaces in and on annular ends. We obtain results which are similar to the ones obtained by Fujimoto ([4], [5]) and Ru ([13], [14]) for (the whole) complete minimal surfaces, thus we show that the restriction of the Gauss map to an annular end of such a complete minimal surface cannot have more branching (and in particular not avoid more values) than on the whole complete minimal surface. We thus give an improvement...
We study the ramification of the Gauss map of complete minimal surfaces in on annular ends. This is a continuation of previous work of Dethloff-Ha (2014), which we extend here to targets of higher dimension.
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