Starts 15 Feb 2023 14:00
Ends 15 Feb 2023 15:00
Central European Time
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ALGEBRAIC GEOMETRY SEMINAR: Gaeta resolutions and strange duality over rational surfaces
Hybrid
Leonardo Building - Luigi Stasi Seminar Room
Registration link:
https://zoom.us/meeting/register/tJUtdumqpjwjGtAzN21XRbOqja09aZKefFci
Abstract: We will discuss resolutions of coherent sheaves by line bundles from strong full exceptional sequences over rational surfaces. We call them Gaeta resolutions. We then apply the results towards the study of the moduli space of sheaves, in particular Le Potier's strange duality conjecture. We will show that the strange morphism is injective in some new cases. One of the key steps is to show that certain Quot schemes are finite and reduced. The next key step is to enumerate the length of the finite Quot scheme, by identifying the Quot scheme as the moduli space of limit stable pairs, where we are able to calculate the (virtual) fundamental class. This is based on joint work with Thomas Goller.
https://zoom.us/meeting/register/tJUtdumqpjwjGtAzN21XRbOqja09aZKefFci
Abstract: We will discuss resolutions of coherent sheaves by line bundles from strong full exceptional sequences over rational surfaces. We call them Gaeta resolutions. We then apply the results towards the study of the moduli space of sheaves, in particular Le Potier's strange duality conjecture. We will show that the strange morphism is injective in some new cases. One of the key steps is to show that certain Quot schemes are finite and reduced. The next key step is to enumerate the length of the finite Quot scheme, by identifying the Quot scheme as the moduli space of limit stable pairs, where we are able to calculate the (virtual) fundamental class. This is based on joint work with Thomas Goller.