Year 2024
 | Seminario Matematico e Fisico di Milano |
| Alexander Kuznetsov
Steklov Institute, Mosca
Categorical resolutions and categorical absorptions of singularities
Thursday, January 18 2024, at 16:30
Aula 8, Dipartimento di Matematica, via Saldini |
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Abstract
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A resolution of singularities of a singular algebraic variety is a proper morphism from a smooth algebraic variety which induces an isomorphism of dense open subsets. An old but extremely important theorem of Hironaka proves that, over a field of characteristic zero, any algebraic variety admits a resolution.
Similarly, an absorption of singularities of a singular algebraic variety is a proper morphism to a smooth algebraic variety which induces an isomorphism of dense open subsets. In contrast to resolution, existence of absorption is a very rare phenomenon.
I will talk about a categorical version of resolution and absorption of singularities, give some examples, and try to demonstrate how useful these notions are.
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