Julian Rosen, Department of Pure Mathematics, University of Waterloo
"Curves on abelian surfaces"
This
talk
will
begin
with
an
introduction
to
abelian
varieties,
which
are
projective
varieties
having
the
structure
of
an
abelian
group.
Abelian
varieties
of
dimension
1
are
elliptic
curves.
Our
focus
will
be
on
abelian
varieties
of
dimension
2.
We
will
discuss
a
correspondence
between
certain
classes
of
line
bundles
on
an
abelian
surface
and
integral
quadratic
forms.
This
correspondence
can
be
used
to
determine
which
genera
of
curves
can
be
embedded
in
various
abelian
surfaces,
and
which
abelian
surfaces
embed
in
the
projective
space
P^4
(every
abelian
surface
embeds
in
P^5).
Some
of
the
answers
are
quite
surprising.
This
talk
is
based
on
joint
work
with
Ari
Shnidman.