October 19 (Thur)
13:30 - 15:00 Eduardo Esteves (IMPA)
-Wind from Rio, V-
"Compactifying the Jacobian", Part 1.
15:30 - 17:00 Fyodor Zak (IUM)
"Bounding numerical invariants of projective varieties", Part 1.
October 20 (Fri)
10:00 - 11:30 Eduardo Esteves (IMPA)
-Wind from Rio, V-
"Compactifying the Jacobian", Part 2.
13:30 - 15:00 Fyodor Zak (IUM)
"Bounding numerical invariants of projective varieties", Part 2.
15:30 - 17:00 Changho Keem (SNU)
"On double covering of special curves".
|
| 19 (Thur)
| 20 (Fri)
|
| 10:00-11:30
| -
| Esteves 2
|
| 13:30-15:00
| Esteves 1
| Zak 2
|
| 15:30-17:00
| Zak 1
| Keem
|
"Compactifying the Jacobian",
Eduardo Esteves (Instituto Nacional de Matematica Pura e Aplicada)
In the first talk, a survey will be given on compactifications of
Jacobian varieties of singular curves, both irreducible and reducible,
going through motivation, definitions and simple properties.
In the second talk, more recent results will be presented about
the compactifications by torsion-free, rank-1 sheaves.
"On double covering of special curves",
Changho Keem (Seoul National University)
In this talk, I would like to present some old and new results
on a curve which admits a morphism of degree two onto another curve.
We will focus on various properties of the classical Brill-Noether loci of special
linear systems on double coverings of hyperelliptic curves.
In particular, we will discuss about the irreducibility, generically reducedness and singular loci of the
Brill-Noether locus on a double covering when the genus of the base curve is rather small.
Furthermore, if time permits, we will also discuss about the existence of the so-called
"primitive linear series" on special curves.
"Bounding numerical invariants of projective varieties",
Fyodor Zak (Independent University of Moscow)
Let X be a nonsingular projective variety of dimension n,
codimension a, and degree d. A natural way to study X is to compute
its numerical invariants, such as Betti and Hodge numbers,
Chern numbers (such as self-itersection of canonical class or Euler characteristic),
classes (in particular, the degree of dual variety) etc.
The problem of what are the possible values of numerical invariants
of X and what is the relationship between various invariants has been
studied for a century and a half, but little was known up to now. In
particular, Castelnuovo found a sharp bound for the genus in the case
when n=1, and the Riemann-Roch-Hirzebruch theorem provides some
relations between certain invariants. In my talk I'll explain how to
extend Castelnuovo's bound to varieties of arbitrary dimension. I'll also
explain why the numericall invariants are all "asymptotically equivalent"
to each other and why, contrary to topologists' belief, the larger the
invariants (e.g. Betti numbers), the simpler is the variety.
Prerequisites: basic algebraic geometry, rudiments of topology
(definition of cell complexes and Betti numbers). For the second talk it
would be helpful to understand the notions of Hodge numbers and Chern classes.
[2006/10/13]