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Counting conics in complete intersections

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 Added by Andreas H\\\"oring
 Publication date 2018
  fields
and research's language is English




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We count the number of conics through two general points in complete intersections when this number is finite and give an application in terms of quasi-lines.



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112 - Fumiaki Suzuki 2015
We prove that every smooth complete intersection X defined by s hypersurfaces of degree d_1, ... , d_s in a projective space of dimension d_1 + ... + d_s is birationally superrigid if 5s +1 is at most 2(d_1 + ... + d_s + 1)/sqrt{d_1...d_s}. In particular, X is non-rational and Bir(X)=Aut(X). We also prove birational superrigidity of singular complete intersections with similar numerical condition. These extend the results proved by Tommaso de Fernex.
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