Stanford Student Algebraic Geometry Seminar (SAGS), Fall 2026

This quarter in SAGS, we are learning about hyperbolicity for families of varieties.

References

• Arnaud Beauville, Le nombre minimum de fibres singulières d’une courbe stable sur P¹. Astérisque 86 (1981).
• Frédéric Campana and Mihai Păun, Foliations with positive slopes and birational stability of orbifold cotangent bundles. Publications Mathématiques de l’IHÉS 129 (2019). arXiv:1508.02456.
• Daniel Litt, Variations of Hodge structure. Notes for the Number Theory Learning Seminar on Shimura Varieties (2013).
• Chris Peters, Arakelov-type inequalities for Hodge bundles. Prépublication de l’Institut Fourier 511 (2000). arXiv:math/0007102.
• Mihnea Popa and Christian Schnell, Viehweg’s hyperbolicity conjecture for families with maximal variation. Inventiones Mathematicae 208, no. 3 (2017). arXiv:1511.00294.
• Christian Schnell, An overview of Morihiko Saito’s theory of mixed Hodge modules. In Representation Theory, Automorphic Forms & Complex Geometry: A Tribute to Wilfried Schmid, International Press (2020). arXiv:1405.3096.
• Christian Schnell, On a theorem of Campana and Păun. Épijournal de Géométrie Algébrique 1 (2017), article 8. arXiv:1704.03034.
• Christian Schnell, MAT 690: Advanced Topics in Algebraic Geometry. Course notes, Stony Brook University, Fall 2019. Lecture 8 and Lecture 9.
• Eckart Viehweg, Arakelov (in)equalities. Surveys in Differential Geometry 13 (2008). arXiv:0812.3350.
• Eckart Viehweg and Kang Zuo, Base spaces of non-isotrivial families of smooth minimal models. In Complex Geometry (Göttingen, 2000), Springer, Berlin (2002). arXiv:math/0103122.
• Kang Zuo, Hodge theory and Higgs bundle on moduli spaces of smooth varieties with semi-ample canonical line bundles, negativity and hyperbolicity. Preprint (2022). arXiv:2201.08015.

Schedule

We meet weekly on Wednesdays, 3–4:30pm, in 384-H, from October 7 through December 9, with a break at 3:30 for tea. There is no meeting on November 25 (Thanksgiving week).

Date	Topic	References	Speaker
Oct 7	Intro + Beauville's theorem	Beauville	Spencer
Oct 14	Higgs bundles	Peters, §1, pp. 3–6. Optional: Schnell, Lecture 4, pp. 18–24.	Ronnie
Oct 21	Arakelov's theorem	Peters, §§2–3, pp. 6–10. Optional: Viehweg, Arakelov (in)equalities, pp. 4–6 (Corollary 3.2 and Lemma 3.3).	Esty
Oct 28	Campana–Păun I	Schnell, On a theorem of Campana and Păun, §§1–3, pp. 2–5 (through Remark 9).	Hikari
Nov 4	Campana–Păun II	Schnell, On a theorem of Campana and Păun, §§4–5, pp. 5–8.	Minghao
Nov 11	Viehweg–Zuo I	TBD	Cole
Nov 18	Viehweg–Zuo II	TBD	TBD
Nov 25	No meeting (Thanksgiving week)
Dec 2	Popa–Schnell I	TBD	TBD
Dec 9	Popa–Schnell II	TBD	TBD