Samenvatting
In this thesis, we study the singularity category as introduced by Orlov in his paper ‘Triangulated categories of singularities and D-branes in Landau-Ginzburg models’ [Orl04]. As thetitle of the paper indicates, he defined this triangulated category for a suffiently nice scheme
so that it would serve as a homological invariant that captures the singular information of
that scheme. Since the singularity category is algebraic in nature – as the quotient of a
derived category – it is difficult to infer geometric information out of it. We will therefore
discuss various results that motivate Orlov’s viewpoint and illustrate that the singularity
category fulfills its intended purpose.
Orlov’s singularity category already occurred in other places in the literature, be it in
different shapes. We will also study these different interpretations, which provide links to
other, neighbouring domains.
| Datum prijs | 30 jun. 2022 |
|---|---|
| Originele taal | Dutch |