Displaying similar documents to “Rational equivalence on some families of plane curves”

Enumerative geometry of divisorial families of rational curves

Ziv Ran (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We compute the number of irreducible rational curves of given degree with 1 tacnode in 2 or 1 node in 3 meeting an appropriate generic collection of points and lines. As a byproduct, we also compute the number of rational plane curves of degree d passing through 3 d - 2 given points and tangent to a given line. The method is ‘classical’, free of Quantum Cohomology.

On the variety of linear series on a singular curve

E. Ballico, C. Fontanari (2002)

Bollettino dell'Unione Matematica Italiana

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Let Y be an integral projective curve with g := p a Y 2 . For all positive integers d , r let W d r Y * A * be the set of all L Pic d Y with h 0 Y , L r + 1 and L spanned. Here we prove that if d g - 2 , then dim W d r Y * A * d - 3 r except in a few cases (essentially if Y is a double covering).

Estimates of the number of rational mappings from a fixed variety to varieties of general type

Tanya Bandman, Gerd Dethloff (1997)

Annales de l'institut Fourier

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First we find effective bounds for the number of dominant rational maps f : X Y between two fixed smooth projective varieties with ample canonical bundles. The bounds are of the type { A · K X n } { B · K X n } 2 , where n = dim X , K X is the canonical bundle of X and A , B are some constants, depending only on n . Then we show that for any variety X there exist numbers c ( X ) and C ( X ) with the following properties: For any threefold Y of general type the number of dominant rational maps f : X Y is bounded above by c ( X ) . ...

The Brauer–Manin obstruction for curves having split Jacobians

Samir Siksek (2004)

Journal de Théorie des Nombres de Bordeaux

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Let X 𝒜 be a non-constant morphism from a curve X to an abelian variety 𝒜 , all defined over a number field k . Suppose that X is a counterexample to the Hasse principle. We give sufficient conditions for the failure of the Hasse principle on X to be accounted for by the Brauer–Manin obstruction. These sufficiency conditions are slightly stronger than assuming that 𝒜 ( k ) and Ш ( 𝒜 / k ) are finite.

Nesting maps of Grassmannians

Corrado De Concini, Zinovy Reichstein (2004)

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

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Let F be a field and G r i , F n be the Grassmannian of i -dimensional linear subspaces of F n . A map f : G r i , F n G r j , F n is called nesting if l f l for every l G r i , F n . Glover, Homer and Stong showed that there are no continuous nesting maps G r i , C n G r j , C n except for a few obvious ones. We prove a similar result for algebraic nesting maps G r i , F n G r j , F n , where F is an algebraically closed field of arbitrary characteristic. For i = 1 this yields a description of the algebraic sub-bundles of the tangent bundle to the projective space P F n .