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Results tagged with curves-and-surfaces
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user 4790
A surface is a generalization of a plane which needs not be flat, that is, the curvature is not necessarily zero. This is analogous to a curve generalizing a straight line
10
votes
Accepted
Does there exist a non-trivial semi-stable curve of genus >1 with only 4 singular fibres
Sheng-Li Tan proved that the answer is negative (see http://arxiv.org/pdf/alg-geom/9411002). This had been conjectured by Beauville.
- 27k
21
votes
Accepted
Can curves differentiate vector bundles on P^2?
Any curve of large enough degree will do. Set $F:= E'\otimes E^{\vee}$; if $d$ is a very large integer, then $\mathrm H^1(F(-d)) = 0$. Take any curve $C$ of degree $d$, and suppose that $E\mid_C$ and …
- 27k