Homepage of Lei Zhang

News and Information

News: 欢迎从事多复变、代数几何的博士申请科大的博后（年薪20万）。

Here are some useful Links .

Here are resources of lectures on extension theory (an application of complex analysis in algebraic geomtry)

For suggestions to graduate students, I agree with and refer to Prof. Liang ，there are some interesting material in Shenxing Zhang's homepage （张神星） .

Teaching

2022 Spring, Modern Algebra （近世代数）

2022 Spring, Commutative Algebra (Exercise，中法班习题课)

2021 Fall, Basic Algebraic Geometry I: Algebraic curves (An introduction to AG), William Fulton

2021 Spring, Modern Algebra

2020 Fall, Basic Algebraic Geometry I: Algebraic curves (An introduction to AG), William Fulton

2020 Spring, Modern Algebra

2019 Fall, Basic Algebraic Geometry 1:Varieties in Projective Space(Igor R.Shafarevich)

2019 Sring, Algebraic Geometry and Arithemetic curves(Qing Liu)

2018 Fall, Complex Variable Functions(（复变函数，严镇军 )

2018 Spring, Riemann Surface （黎曼曲面导引，梅加强）

Research

My research area is Algebraic Geometry, and study topics: Algebraic Surface, Irregular Variety, Minimal Model Theory in positive characteristic. Recently my research interest is the classification of varieties in characteristic p.

Accepted papers:

[18] Yi Gu, Lei Zhang and Yongming Zhang, Counterexamples to Fujita's conjecture on surfaces in positive characteristic, accepted by Advances in Mathematics . arXiv: 2002. 04584.

[17] Paolo Cascini, Sho Ejiri, Janos Kollar and Lei Zhang , Subadditivity of Kodaira dimension does not hold in positive characteristic, Commentarii Mathematici Helvetici 96 (2021), no. 3, 465--481. arXiv: 2003. 13206.

[16] Lei Zhang , Abundance for 3-folds with non-trivial Albanese maps in positive characteristic, Journal of the European Mathematical Society 22 (2020), no. 9, 2777--2820. arXiv: 1705.00847.

[15] Lei Zhang , Subadditivity of Kodaira dimensions for fibrations of three-folds in positive characteristics, Advances in Mathematics 354, (2019), https://doi.org/10.1016/j.aim.2019.106741.

[14] C.D. Hacon, Z. Patakfalvi and L. Zhang , Birational characterization of abelian varieties and ordinary abelian varieties in characteristic p > 0, Duke Mathematical Journal 168 (9) (2019), 1723--1736.

[13] Chenyang Xu and Lei Zhang , Nonvanishing for threefolds in characteristic p>5, Duke Mathematical Journal , 168 (7) (2019),1269--1301.

[12] Lei Zhang , Abundance for non-uniruled 3-folds with non-trivial Albanese maps in positive characteristics, Journal of the London Mathematical Society , 99 (2) (2019), no. 2, 332--348.

[11] Yong Hu and Lei Zhang , Surfaces with p_g = q= 1, K^2 = 6 and non-birational bicanonical maps, Acta Mathematica Sinica (English Series) 35 (3) (2019), 321--337.

[10] Sho Ejiri and Lei Zhang , Iitaka's conjecture for 3-folds in positive characteristic, Mathematical Research Letters 25 (2018), 783--802.

[9] Lei Zhang , A note on Iitaka's conjecture C_{3,1} in positive characteristics, Taiwanese Journal of Mathematics ,21 (2017), 689--704.

[8] Caucher Birkar, Yifei Chen and Lei Zhan g, Iitaka's C_{n,m} conjecture for 3-folds over finite fields, Nagoya Mathematical Journal 229 (2018), 21--51.

[7] Lei Zhang , Surfaces with p_g=q = 1, K^2 = 7 and nonbirational bicanonical maps, Geometriea Dedicata 177 (2015), 293--306.

[6] Yifei Chen and Lei Zhang , The subadditivity of the Kodaira dimension for fibrations of relative dimension one in positive characteristic, Mathematical Research Letters 22 (2015), 675--696.

[5] Lei Zhang , The cohomological support locus of pluricanonical sheaves and the Iitaka fibration, Journal of the London Mathematical Society 90 (2014), 592--608.

[4] Lei Zhang , A note on the linear systems on the projective bundles over abelian varieties, Proceedings of the American Mathematical Society 142 (2014), 2569--2580.

[3] Lei Zhan g, On the bicanonical map of primitive varieties with q(X) = dim X: the degree and the Euler number, Mathematische Zeitschrift 277 (2014), 575--590.

[2] Jin-xing Cai, Wenfei Liu and Lei Zhang , Automorphisms of surfaces of general type with q>= 2 acting trivially in cohomology, Compositio Mathematica 149 (2013), 1667--1684.

[1] Lei Zhang , Characterization of a class of surfaces with p_g=0 and K^2 = 5 by their bicanonical maps, Manuscripta Mathematica 135 (2011), 165--181.