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The variation of the rank of elliptic curves over $ℚ$ in families of quadratic twists has been extensively studied by Gouvêa, Mazur, Stewart, Top, Rubin and Silverberg. It is known, for example, that any elliptic curve over $ℚ$ admits infinitely many quadratic twists of rank $\geq 1$ . Most elliptic curves have even infinitely many twists of rank $\geq 2$ and examples of elliptic curves with infinitely many twists of rank $\geq 4$ are known. There are also certain density results. This paper studies the variation of the...

The rank of the multiplication map for sections of bundles on curves

E. Ballico (2001)

Bollettino dell'Unione Matematica Italiana

Sia $X$ una curva liscia di genere $g \geq 2$ ed $A$ , $B$ fasci coerenti su $X$ . Sia $μ_{A, B} : H^{0} (X, A) \otimes H^{0} (X, B) \to H^{0} (X, A \otimes B)$ l'applicazione di moltiplicazione. Qui si dimostra che $μ_{A, B}$ ha rango massimo se $A ≅ ω_{X}$ e $B$ è un fibrato stabile generico su $X$ . Diamo un'interpretazione geometrica dell'eventuale non-surgettività di $μ_{A, B}$ quando $A, B$ sono fibrati in rette generati da sezioni globali e $\deg (A) + \deg (B) \geq 3 g - 1$ . Studiamo anche il caso $dim (Coker (μ_{A, B})) \geq 2$ .

The Riemann-Roch Theorem and the Independence of the Conditions of Adjointness in the case of a curve for which the tangents at the multiple points are distinct from one another.

J.C. Fields (1902)

Journal für die reine und angewandte Mathematik

The Riemann-Roch theorem on algebraic curves

Herbert Schröder (1988/1989)

Séminaire de théorie spectrale et géométrie

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The Picard group of the moduli of higher spin curves.

The polynomial $x^{3} + x^{2} + x - 1$ and elliptic curves of conductor 11

The p-Primary Component of the Cuspidal Divisor Class Group on the Modular Curve X(p).

The practical determination of the deficiency (Geschlecht) and adjoint ... curves for a Riemann surface

The p-Rank of Artin-Schreier Curves.

The product of $N$ linear forms in a field of series and the Riemann hypothesis for curves

The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".

The projectivity of the moduli space of stable curves, II: The stacks M...

The projectivity of the moduli space of stable curves, III: The line bundles on M..., and a proof of the projectivity of M... in characteristic 0.

The Prym variety for a cyclic unramified cover of a hyperelliptic Riemann surface.

The Prym vector bundle and Gunning vector bundle over the Teichmüller space.

The rank of hyperelliptic Jacobians in families of quadratic twists

The rank of the multiplication map for sections of bundles on curves

The rank-one limit of the Fourier-Mukai transform.

The rationality of some moduli spaces of plane curves

The real genus of the alternating groups.

The reduction of a double covering of a Mumford curve.

The Riemann surface of a uniform dessin.

The Riemann-Roch Theorem and the Independence of the Conditions of Adjointness in the case of a curve for which the tangents at the multiple points are distinct from one another.

The Riemann-Roch theorem on algebraic curves

Currently displaying 141 – 160 of 250