Assistant Professor,
CV
Mathematical Institute
Utrecht University
P.O. Box 80010
3508 TA Utrecht
The Netherlands
Hans Freudenthalgebouw, Room 502
m.kool1@uu.nl
Algebraic geometry. I am interested in moduli spaces of sheaves (or sheaf-like objects) on specific classes of varieties (e.g. toric varieties, local surfaces, elliptic fibrations, general type surfaces). Explicit descriptions of strata in these moduli spaces, or (virtual) cycles on them, can be used for calculating invariants such as topological Euler characteristics or Donaldson-Thomas, Pandharipande-Thomas, or Donaldson invariants. This often leads to unexpected links with other fields such as enumerative geometry, modular forms, combinatorics, or theoretical physics.
Organization: See organizational e-mail. Material covered and exercises:
- Jan 8: Ch. 1-4 of Armstrong. Exc. 1.3, 1.4, 2.3, 2.7, 2.8, 3.2, 3.7*, 4.1, 4.6*, 4.8. Markers: Djin, Marije, Thomas.
- Jan 9: Ch. 5, 6 of Armstrong. Exc. 5.4, 5.5, 5.6, 6.2, 6.6*, 6.9*. Markers: Geofrey, Pepijn, Friso.
- Jan 10: parts of Ch. 7, 8 of Armstrong. Exc. 7.2, 7.11, 7.12*, 8.1, 8.6, 8.4*. Markers: Karel, Max, Thijs.
- Jan 11: Ch. 10, 11 of Armstrong. Exc. 10.7, 10.12*, 11.1*, 11.3, 11.4. Markers: Nour, Hannah, Marijn.
- Jan 12: Ch. 12, 15, 16 of Armstrong (we skipped 9, 13, 14). Exc. 12.1, 12.6, 12.9*, 15.2, 15.6*, 15.7. Markers: Alidad, Nick, and Louis.
Course information on Blackboard.
Cursusinformatie op Blackboard.