Theta-duality on Prym varieties and a Torelli Theorem

Let $\pi : \widetilde C \to C$ be an unramified double covering of irreducible smooth curves and let $P$ be the attached Prym variety. We prove the scheme-theoretic theta-dual equalities in the Prym variety $T(\widetilde C)=V^2$ and $T(V^2)=\widetilde C$, where $V^2$ is the Brill-Noether locus of $P$ associated to $\pi$ considered by Welters. As an application we prove a Torelli theorem analogous to the fact that the symmetric product $D^{(g)}$ of a curve $D$ of genus $g$ determines the curve.

A lower bound in Nehari's theorem on the polydisc

By theorems of Ferguson and Lacey ($d=2$) and Lacey and Terwilleger ($d>2$), Nehari's theorem is known to hold on the polydisc $\D^d$ for $d>1$, i.e., if $H_\psi$ is a bounded Hankel form on $H^2(\D^d)$ with analytic symbol $\psi$, then there is a function $\varphi$ in $L^\infty(\T^d)$ such that $\psi$ is the Riesz projection of $\varphi$. A method proposed in Helson's last paper is used to show that the constant $C_d$ in the estimate $\|\varphi\|_\infty\le C_d \|H_\psi\|$ grows at least exponentially with $d$; it follows that there is no analogue of Nehari's theorem on the infinite-dimensional polydisc.

Median rituaalit ja moderni pyhyys : kuoliko Michael Jackson pyhän uhrikuoleman?

Kirjallisuusarvostelu

Dr. John Jackson

Professor of Geography.

Dr. Jackson

Professor Jackson at his desk.

Reflections upon the late correspondence between Mr. Secretary Smith, and Francis James Jackson, esq., Minister Plenipotentiary of His Britannic Majesty /

Originally published in the Federal Republican of Baltimore.

Resolutions reported by the Military Committee, expressive of the thanks of Congress to Major General Jackson, and the troops under his command, for their gallantry and good conduct, in the defence of New Orleans.--

February 13, 1815. Printed by order of the Senate of the United States.

Reflections upon the late correspondence between Mr. Secretary Smith, and Francis James Jackson, esq., Minister Plenipotentiary of His Britannic Majesty

Originally published in the Federal Republican of Baltimore. Printed by Benjamin Edes

Resolutions reported by the Military Committee, expressive of the thanks of Congress to Major General Jackson, and the troops under his command, for their gallantry and good conduct, in the defence of New Orleans

February 13, 1815. Printed by order of the Senate of the United States. Printed by Roger C. Weightman