University of Cambridge > > Kuwait Foundation Lectures > The shape of an algebraic variety

The shape of an algebraic variety

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact Helen Innes.

An algebraic variety X over the complex numbers has, as one of its main facets, a topological space $X$. The study of $X{\rm top}$ has played an important role in the history of algebraic geometry. We will present a way of measuring the “shape” of $X$ by considering maps from it into different targets. The targets T, which are like spaces, are also profitably viewed as n-stacks, a notion from higher category theory. The complex algebraic structure of X leads to a number of different structures on $Hom(X{\rm top},T)$. For example when $T=BG$, the mapping stack $Hom(X^{\rm top},BG)$ may be viewed as the moduli space of G-bundles with integrable connection, or principal G-Higgs bundles. These fit together into Hitchin’s twistor space. Consideration of these structures is a good way of organizing the investigation of the topology of complex algebraic varieties.

This talk is part of the Kuwait Foundation Lectures series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2023, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity