arXiv subjects

Remke Kloosterman

Publications and source records attributed to Remke Kloosterman.

39 records · Page 3Linked to original sources

arXiv2004

A new model for the theta divisor of the cubic threefold

In this paper we give a birational model for the theta divisor of the intermediate Jacobian of a generic cubic threefold $X$. We use the standard realization of $X$ as a conic bundle and a $4-$dimensional family of plane quartics which are totally tangent to the discriminant quintic curve of such a conic bundle structure. The additional data of an even theta characteristic on the curves in the family gives us a model for the theta divisor.

math.AG↗

arXiv2003

Extremal elliptic surfaces & Infinitesimal Torelli

We describe in terms of the j-invariant all elliptic surfaces pi: X -> C with a section, such that h^{1,1}(X)=rank NS(X) and the Mordell-Weil group of pi is finite. We use this to give a complete solution to infinitesimal Torelli for elliptic surfaces with a section over P^1.

math.AG↗

arXiv2003

The p-part of Tate-Shafarevich groups of elliptic curves can be arbitrarily large

In this paper it is shown that for every prime p>5 the dimension of the p-torsion in the Tate-Shafarevich group of E/K can be arbitrarily large, where E is an elliptic curve defined over a number field K, with [K:Q] bounded by a constant depending only on p. From this we deduce that the dimension of the p-torsion in the Tate-Shafarevich group of A/Q can be arbitrarily large, where A is an abelian variety, with dim A bounded by a constant depending only on p.

math.NT↗