Welcome to Tong's Homepage

• Welcome
• Seminar
• Short Course on Arithmetic Geometry
• Research
• Teaching
• Links
• About me

Research interest:

I am mainly working on Arakelov geometry and algebraic geometry, but I am also interested in other subjects related to arithmetic algebraic geometry.

Publication:

• Relative Clifford inequality for varieties fibered by curves,
Journal of Differential Geometry, Vol. 112, No. 2 (2022), 341-376.
• Relative Severi inequality for fibrations of maximal Albanese dimension over curves, (with Yong Hu)
Forum of Mathematics, Sigma, Vol. 10, (2022), Paper No. e45.
• Noether-Severi inequality and equality for irregular threefolds of general type, (with Yong Hu)
Journal für die reine und angewandte Mathematik, Vol. 787, (2022), 241-273.
• Fibered varieties over curves with low slope and sharp bounds in dimension three, (with Yong Hu)
Journal of Algebraic Geometry, Vol. 30, No. 1 (2021), 57-95.
• Sakai's Theorem for Q-divisors on surfaces and applications, (with Fei Ye and Zhixian Zhu)
Asian Journal of Mathematics, Vol. 22, No. 4 (2018), 761-785 (special issue dedicated to Professor Ngaiming Mok’s 60th birthday).
• Slope inequality for families of curves over surfaces,
Mathematische Annalen, Vol. 371, No. 3-4 (2018), 1095-1136.
• Effective bound of linear series on algebraic and arithmetic varieties, (with Xinyi Yuan)
Journal für die reine und angewandte Mathematik, Vol. 736, (2018), 255-284.
• Irregular varieties of Albanese fiber dimension one with small volume,
Mathematical Research Letters, Vol. 23, No. 6 (2016), 1833-1856.
• Geography of irregular Gorenstein 3-folds,
Canadian Journal of Mathematics, Vol. 67, No. 3 (2015), 696-720.
• Severi inequality for varieties of maximal Albanese dimension,
Mathematische Annalen, Vol. 359, No. 3-4 (2014), 1097-1114.
• Relative Noether inequality on fibered surfaces, (with Xinyi Yuan)
Advances in Mathematics, Vol. 259, No. 10 (2014), 89-115.
• Effective bound of linear series on arithmetic surfaces, (with Xinyi Yuan)
Duke Mathematical Journal, Vol. 62, No. 10 (2013), 1723-1770.
• Adjoint linear systems on algebraic surfaces,
International Journal of Mathematics, Vol. 24, No. 3 (2013), 14 pages.

Paper accepted:

• Algebraic threefolds of general type with small volume, (with Yong Hu)
Mathematische Annalen, to appear, arXiv: 2204.02222.

Expository paper:

• Geography of irregular varieties of general type: some recent results,
Proceedings of the Seventh International Congress of Chinese Mathematicians. Vol. II, 169-188, Advanced Lectures in Mathematics (ALM), 44, Int. Press, Somerville, MA, 2019.

Preprint:

• Threefolds on the Noether line and their moduli spaces, (with Stephen Coughlan, Yong Hu and Roberto Pignatelli)
preprint, arXiv: 2409.17847.
• Noether inequality for irregular threefolds of general type, (with Yong Hu)
preprint, arXiv: 2402.17468.