seminars of Algebraic geometry

[Emilia Mezzetti]

UNIVERSITA' DI TRIESTE
DIPARTIMENTO DI MATEMATICA E INFORMATICA

SEMINARS ANNOUNCEMENT

On Tuesday March 11 2008 the following seminars will be given:


14.30: Remke KLOOSTERMAN (Leibniz Universitaet Hannover)

The Mordell-Weil group of elliptic threefolds
(joint w. K. Hulek)

15.45: Orsola Tommasi (Leibniz Universitaet Hannover)

Hypersurfaces with too many lines

Venue: Room 4A of the Dept of Mathematics and Informatics (H2 
building, Via Valerio 12/1, 4th floor).
Everybody interested is much welcome to attend.

Abstracts of the seminars

Kloosterman: Let pi:X->B be an elliptic fibration with section. The 
most important
invariants of pi are its configuration of singular fibres and the group
MW(pi) of rational sections. The configuration of singular fibres is
well-understood, whereas the determination of MW(pi) remains mysterious.
One knows that MW(pi) is finitely generated unless X is birational to a
product E x B.
In the case that B is a curve, there exist methods to determine MW(pi),
but these methods turn out to work only in particular cases.
In this talk, we present a method to determine MW(pi) if B is a 
rational surface and X is sufficiently general.
The determination of MW(pi) is expected to be useful for solving
problems like constructing elliptic curves E/Q such that E(Q) has large
rank; for identifying hyperelliptic curves that are dangerous for
hyperelliptic curve cryptography; but also for solving the following
problem:
For every integer r, does there exist an hyperelliptic curve C such
that its Jacobian is isogenous to E^r x A?

Tommasi: The study of rational curves on algebraic varieties is an 
important area of research in algebraic geometry. In this talk we 
will concentrate on a specific problem: What is the maximal dimension 
for a family of lines lying on a nonsingular hypersurface of given 
degree in projective space? We will present the conjectures on this 
subject formulated by Debarre-De Jong and Beheshti-Starr, and outline 
a construction that gives a geometric explanation of why these 
conjectures should be true. This is joint work (in progress) with J. 
M. Landsberg, Texas A&M University.


-- 
Prof. Emilia Mezzetti

Dipartimento di Matematica e Informatica
Universita' di Trieste
Via Valerio 12/1
34127 Trieste, Italia

Stanza 227, II piano
e-mail: mezzette at units.it
tel. studio (+39) 040 558 2650
skype: emiliamezzetti
tel. Segreteria Dip.: (+39) 040 558 2635 oppure 2618
fax: (+39) 040 558 2636
http://www.dmi.units.it/~mezzette/