Jacobian factors in any ranks and DAHA superpolynomials

開催日時
2018/06/08 金 16:30 - 18:00
場所
RIMS402号室
講演者
Ivan Cheredink
講演者所属
Chapell Hill/Kyoto
概要

The theory of the moduli spaces of torsion free
sheaves in any ranks over singular curves is quite
a challenge, including nodal curves and rk=2
(Gieseker, Bertram, others). Its local counterpart is
the theory of affine Springer fibers for non-reduced
(germs of) singular curves, which is unsettled too.

For type A and in the nil-elliptic case, these fibers can
be identified with the Jacobian factors, which are simple
to define projective(!) varieties, though this approach
was not extended to higher ranks as well. For plane
curve singularities (spectral curves are of this kind in
type A), there is a strong support: the corresponding
geometric superpolynomials are expected to coincide
with the DAHA superpolynomials colored by columns,
and through them to be connected with any other
theories of superpolynomials, including the original
(uncolored) ones due to Khovanov-Rozansky.

I will define in this talk Jacobian factors in any ranks and
state their connection with the DAHA superpolynomials.
This is joint with Ian Philipp. The connection conjecture
was checked in many cases and a general proof seems
doable (at least in the motivic setting, to be explained).