Collected Works of Max Planck

Collected Works

This paper provides empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves. The second of theseconjectures relates six quantities associated to a Jacobian over the rationalnumbers. One of these six quantities is the size of the Shafarevich-Tate group.Unable to compute that, we computed the five other quantities and solved for...

The Collected Works of

P M Max − Planck −

Klein's Collected Works

Felix Klein: Gesammelte mathematische Abhandlungen. Vol. 1. Liniengeometrie, Grundlegung der Geometrie, Zum Erlanger Programm. Edited by R. Fricke and A. Ostrowski. Berlin, Julius Springer, 1921. xiii + 612 pages. Felix Klein, born at Düsseldorf, April 25,1849, was awarded the doctor's degree December 12, 1868, by the University of Bonn. The dissertation was directed and the examination conduct...

Max - Planck - Institut für

In this paper we consider the question of determining the geometric genera of irreducible curves lying on a very general surface S of degree d > 5 in P (the cases d 6 4 are well known). For any d > 4 we introduce the set Gaps(d) of all non–negative integers which are not realized as geometric genera of irreducible curves on a very general surface of degree d in P. We prove that Gaps(d) is finit...