ICTP Algebraic Geometry Seminar - Wednesday 9 November, at 16:00 (Yulieth Prieto Montanez)/hybrid seminar

[ICTP Math Section]

ALGEBRAIC  GEOMETRY SEMINARS  2022

hybrid seminar

Wednesday 9 November, at 16:00 hrs.

Register in advance for this meeting:
https://zoom.us/meeting/register/tJYpcOyuqjovGtairkDg-0xtWjPdhgFEQMwz
After registering, you will receive a confirmation emailcontaining
information about joining the meeting.


Yulieth Prieto Montanez (ICTP)


I: On the geometry of hyperkähler manifolds

Compact hyperkähler (HK) manifolds (also known as Irreducible 
holomorphic symplectic manifolds) are higher-dimensional analogs of K3 
surfaces generalising many of their properties. However, one of the most 
valuable theorems, the Torelli theorem for K3 surfaces, is slightly 
different from the case of HK manifolds. In this part, we introduce some 
of the main facts about HK manifolds, the known examples, and the notion 
of deformation type, which is crucial in order to construct new examples 
of such varieties. In particular, we focus on the moduli space of stable 
sheaves of K3 surfaces, which is an example introduced in the seminal 
works by Mukai and later continued by Göttsche-Huybrechts, O'Grady, and 
Yoshioka.

II: The birational geometry of hyperkähler manifolds of K3-n type 
admitting symplectic actions

In this second part, we study a particular type of deformation of HK 
manifolds admitting a special property: they carry a non-trivial 
symplectic birational map. We will see that using some standard facts in 
lattice theory, such varieties are birational to the moduli space of 
stable sheaves on K3 surfaces. Furthermore, by applying techniques in a 
setting of Bridgeland stability conditions, we can prove that they are 
isomorphic to some moduli spaces. This last part motivated us to study 
the wall-crossing of such moduli spaces in order to characterize their 
Mukai vectors. This is a work in collaboration with D. Mattei and Y. Dutta.

VENUE:  Luigi Stasi Seminar Room (ICTP Leonardo da Vinci Building, first 
floor), for those wishing to attend in person.

https://indico.ictp.it/event/10118/

https://researchseminars.org/


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