E Frenkel
Vertex algebras and Algebraic Curves
Abstract:
Vertex algebras are algebraic objects that formalize the concepts
of vertex operators and operator product expansion from
two-dimensional conformal field theory. In this lectures we will
give the definition of vertex algebra and consider some examples.
We will then give a coordinate independent description of the
vertex operators. This will allow us to define the spaces of
coinvariants and conformal blocks for a general vertex algebra and
an arbitrary pointed algebraic curve. When the complex structure of
the curve and other geometric data are varied, these spaces combine
into a sheaf on the relevant moduli space. From this perspective,
vertex algebras appear as the algebraic objects that encode the
geometric structure of various moduli spaces associated with
algebraic curves.
math.AG/0303074
lecture:
|
|
