ALGEBRAIC GEOMETRY SEMINAR @ SISSA - Tuesday, 21 January, at 16:00 (Carlo SCARPA)

[ICTP Math Section]

ALGEBRAIC   GEOMETRY   SEMINAR


Venue: SISSA, Lecture room (A-134)


Tuesday 21 January, at 16:00 hrs.


Speaker: Carlo Scarpa (SISSA)


Title: An analogue of Hitchin's equations in the category of polarized 
varieties


Abstract: The Hitchin-Kobayashi correspondence states that the moduli 
space of stable vector bundles over a projective manifold coincides with 
the moduli space of Einstein-Hermitian vector bundles. Over the years, 
this result and its consequences have served as a motivation to relate 
the existence of metrics of constant curvature on polarized manifolds to 
an algebraic condition (K-stability).
The correspondence between stable and Einstein-Hermitian vector bundles 
has a well-known generalization in the context of Higgs bundles, where 
one studies Hitchin's harmonic bundle equations. In this talk we will 
describe how to give an analogous construction in the category of 
polarized varieties, thus defining what a "Higgs field" should be in 
this context and studying a system of equations that naturally arises 
from the construction.

Note: After the talk we will be discussing the future plans for the seminar.

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