Ph.D. Course 
Fibered varieties
Pavia – Milano Bicocca – INdAM Ph.D. program in Mathematics
 
Teachers. Roberto Pignatelli, Lidia Stoppino
Overview. The course is devoted to the study of the algebraic varieties having a fibration on a variety of smaller dimension.
The prerequisites are basics of sheaf theory and Cech cohomology
When. January-February 2025
Tentative schedule:
January

Wednesday 22, 10-12
Thursday 23, 14-16
Friday 24, 10-12 
Wednesday 29, 15-17
Thursday 30, 15-17 
Friday 31, 10-12 

February
Tuesday 18, 14-16 
Wednesday 19, 10-12 
Thursday 20, 14-16

Tuesday  25, 10-12 
Wednesday 26, 10-12 
Thursday 27. 10-12
Where. Pavia, Departement of Mathematics, aula seminari paino C (C12-C13 primo piano)

Attenzione: se qualcuno ha bisogno di seguire in streaming parte del corso scriva tempestivamente  a Lidia Stoppino per avere il link zoom!
Contacts. roberto.pignatelli@unitn.it, lidia.stoppino@unipv.it
Tentative program:
In the first part of the course, we will quickly revisit the concepts of Spec and Proj and discuss some important examples, such as weighted projective spaces.
In the second part, we will explore the concept of bundles in algebraic geometry and its connection with the construction known as relative Proj, with a particular focus on bundles in weighted projective spaces. 
Finally, examples of hypersurfaces in such fibrations, which are relevant from the perspective of the study of the moduli spaces of varieties of general type, will be discussed.
 
References (in ordine di comparizione)
 
  • Eisenbud, I, Harris, J. The geometry of schemes, GTM, Springer-Verlag New York 2000, X, 294 pp.

  • Dolgachev, I. (1982). Weighted Projective Varieties. Lect. Notes in Math. Vol. 956. Berlin-Heidelberg, New York: Springer-Verlag, pp. 34–71.
  • Grothendieck, A.Eléments de géométrie algébrique. II. Etude globale elémentaire de quelques  classes de morphismes. Inst. Hautes Etudes Sci. Publ. Math. No. 8 (1961), 222 pp.
  •  Coughlan, S., Pignatelli, R., Simple fibrations in (1,2)-surfaces, Forum of Mathematics, Sigma, Volume 11, 2023, e43. https://doi.org/10.1017/fms.2023.41
  • Rana, J., Rollenske, S., Standard stable Horikawa surfaces, Algebr. Geom. 11 (2024), no. 4, 569–592.
  • Coughlan, S., Hu, Y., Pignatelli, R., Zhang, T., Threefolds on the Noether line and their moduli spaces, arXiv:2409.17847 (2024).
  • Pignatelli, R.,  On canonical threefolds near the Noether line, arXiv:2410.06009 (2024)