(pre)publications

  1. (With Andrei Neguț and Georg Oberdieck) Motivic decompositions for the Hilbert scheme of points of a K3 surface. arXiv:1912.09320.
  2. (With Andrew Harder, Zhiyuan Li, and Junliang Shen) P = W for Lagrangian fibrations and degenerations of hyper-Kähler manifolds. arXiv:1908.07510.
  3. (With Junliang Shen) Topology of Lagrangian fibrations and Hodge theory of hyper-Kähler manifolds. arXiv:1812.10673.
  4. (With Georg Oberdieck and Junliang Shen) Rational curves in holomorphic symplectic varieties and Gromov-Witten invariants. Adv. Math. 357 (2019), 106829, 28 pp.
  5. (With Junliang Shen) K3 categories, one-cycles on cubic fourfolds, and the Beauville-Voisin filtration. J. Inst. Math. Jussieu, to appear.
  6. (With Dan Petersen and Mehdi Tavakol) Tautological classes with twisted coefficients. arXiv:1705.08875.
  7. (With Junliang Shen and Xiaolei Zhao) Derived categories of K3 surfaces, O'Grady's filtration, and zero-cycles on holomorphic symplectic varieties. Compos. Math. 156 (2020), no. 1, 179-197.
  8. (With Rahul Pandharipande) Relations in the tautological ring of the moduli space of K3 surfaces. J. Eur. Math. Soc. (JEMS) 22 (2020), no. 1, 213-252.
  9. (With Nebojsa Pavic and Junliang Shen) On O'Grady's generalized Franchetta conjecture. Int. Math. Res. Not. IMRN (2017), no. 16, 4971-4983.
  10. (With Zhi Jiang) On the Chow ring of certain rational cohomology tori. C. R. Math. Acad. Sci. Paris 355 (2017), no. 5, 571-576.
  11. (With Yi Zhu) A1-equivalence of zero cycles on surfaces, II. Ann. K-Theory 3 (2018), no. 3, 379-393.
  12. (With Jim Bryan, Georg Oberdieck, and Rahul Pandharipande) Curve counting on abelian surfaces and threefolds. Algebr. Geom. 5 (2018), no. 4, 398-463.
  13. Cycles on curves and Jacobians: a tale of two tautological rings. Algebr. Geom. 3 (2016), no. 2, 179-210.
  14. (With Ben Moonen) Some remarks on modified diagonals. Commun. Contemp. Math. 18 (2016), no. 1, 1550009, 16 pp.
  15. Finite-dimensionality and cycles on powers of K3 surfaces. Comment. Math. Helv. 90 (2015), no. 2, 503-511.
  16. Tautological cycles on curves and Jacobians. PhD thesis, Université Paris VI and Radboud Universiteit Nijmegen, 2013.
  17. The generic nontriviality of the Faber-Pandharipande cycle. Int. Math. Res. Not. IMRN (2015), no. 5, 1263-1277.

spring 2020

NEW! Video lectures are available here, and some handwritten notes are here. If you still wish to join our WeChat group, please contact the teaching assistant/group owner Guo Hanfei.

This semester I teach Geometry II (honors). Our main reference is:

Miles Reid, Undergraduate algebraic geometry. London Mathematical Society Student Texts, 12. Cambridge University Press, Cambridge, 1988. viii+129 pp.

Here are some other references:

  1. C. Herbert Clemens, A scrapbook of complex curve theory. Second edition. Graduate Studies in Mathematics, 55. American Mathematical Society, Providence, RI, 2003. xii+188 pp.
  2. Klaus Hulek, Elementary algebraic geometry. Translated from the 2000 German original by Helena Verrill. Student Mathematical Library, 20. American Mathematical Society, Providence, RI, 2003. viii+213 pp.
  3. Frances Kirwan, Complex algebraic curves. London Mathematical Society Student Texts, 23. Cambridge University Press, Cambridge, 1992. viii+264 pp.

contact info

BICMR, Peking University
78306 Jingchunyuan Courtyard 78
5 Yiheyuan Road, Haidian District
Beijing 100871, China

qizheng@math.pku.edu.cn

+86 (10) 6274 4086