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The dimension growth conjecture

  • Timothy D. Browning
Part of the Progress in Mathematics book series (PM, volume 277)

Abstract

For any n≥3, let V⊂ℙn−1 be an irreducible variety of degree d whose ideal is generated by forms defined over the rationals. In this degree of generality one might still ask whether anything meaningful can be said about the corresponding counting function N v (B), as defined in (1.6). In contrast to the preceding chapter, where precise asymptotic formulae were sought for N U (B) for suitable open subsets UV, the aim of the present chapter is to seek general upper bounds for the full counting function N V (B), making as few assumptions on V as possible.

Keywords

Linear Space Irreducible Component Singular Locus Hyperplane Section Fano Variety 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag AG 2009

Authors and Affiliations

  • Timothy D. Browning
    • 1
  1. 1.School of MathematicsUniversity of BristolBristolUK

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