Frédéric Han (2010)
Annales de l’institut Fourier
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We study the geometry of a general Fano variety of dimension four, genus nine, and Picard number one. We compute its Chow ring and give an explicit description of its variety of lines. We apply these results to study the geometry of non quadratically normal varieties of dimension three in a five dimensional projective space.
Mattias Jonsson, Mircea Mustaţă (2012)
Annales de l’institut Fourier
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We study asymptotic jumping numbers for graded sequences of ideals, and show that every such invariant is computed by a suitable real valuation of the function field. We conjecture that every valuation that computes an asymptotic jumping number is necessarily quasi-monomial. This conjecture holds in dimension two. In general, we reduce it to the case of affine space and to graded sequences of valuation ideals. Along the way, we study the structure of a suitable valuation space. ...
Gueorgui Tomov Todorov (2007)
Annales de l’institut Fourier
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In this paper we will prove that for a threefold of general type and large volume the second plurigenera is positive and the fifth canonical map is birational.
Greg W. Anderson (2007)
Annales de l’institut Fourier
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For each global field of positive characteristic we exhibit many examples of two-variable algebraic functions possessing properties consistent with a conjectural refinement of the Stark conjecture in the function field case recently proposed by the author. All the examples are Coleman units. We obtain our results by studying rank one shtukas in which both zero and pole are generic, i. e., shtukas not associated to any Drinfeld module.
Frédéric Campana, Vincent Koziarz, Mihai Păun (2012)
Annales de l’institut Fourier
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In this note we show that, for any log-canonical pair , is -effective if its Chern class contains an effective -divisor. Then, we derive some direct corollaries.