Displaying similar documents to “Higher order contact of real curves in a real hyperquadric. II”

An iterative construction for ordinary and very special hyperelliptic curves

Francis J. Sullivan (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Si costruiscono famiglie di curve iperellittiche col p —rango della varietà jacobiana uguale a zero. La costruzione sfrutta le proprietà elementari dell’operatore di Cartier e delle estensioni p -cicliche dei corpi con la caratteristica p maggiore di zero.

The Analytic Rank of a Family of Jacobians of Fermat Curves

Tomasz Jędrzejak (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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We study the family of curves F m ( p ) : x p + y p = m , where p is an odd prime and m is a pth power free integer. We prove some results about the distribution of root numbers of the L-functions of the hyperelliptic curves associated to the curves F m ( p ) . As a corollary we conclude that the jacobians of the curves F m ( 5 ) with even analytic rank and those with odd analytic rank are equally distributed.

Invariants of real symplectic four-manifolds out of reducible and cuspidal curves

Jean-Yves Welschinger (2006)

Bulletin de la Société Mathématique de France

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We construct invariants under deformation of real symplectic four-manifolds. These invariants are obtained by counting three different kinds of real rational J -holomorphic curves which realize a given homology class and pass through a given real configuration of (the appropriate number of) points. These curves are cuspidal curves, reducible curves and curves with a prescribed tangent line at some real point of the configuration. They are counted with respect to some sign defined by the...

Labeled floor diagrams for plane curves

Sergey Fomin, Grigory Mikhalkin (2010)

Journal of the European Mathematical Society

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Floor diagrams are a class of weighted oriented graphs introduced by E. Brugallé and the second author. Tropical geometry arguments lead to combinatorial descriptions of (ordinary and relative) Gromov–Witten invariants of projective spaces in terms of floor diagrams and their generalizations. In a number of cases, these descriptions can be used to obtain explicit (direct or recursive) formulas for the corresponding enumerative invariants. In particular, we use this approach to enumerate...

On quadratically integrable solutions of the second order linear equation

T. Chantladze, Nodar Kandelaki, Alexander Lomtatidze (2001)

Archivum Mathematicum

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Integral criteria are established for dim V i ( p ) = 0 and dim V i ( p ) = 1 , i ∈ { 0 , 1 } , where V i ( p ) is the space of solutions u of the equation u ' ' + p ( t ) u = 0 satisfying the condition ∫ + ∞ u 2 ( s ) s i d s < + ∞ .