All Outputs (3)

Sakai's theorem for Q-divisors on surfaces and applications (2018)
Journal Article
Ye, F., Zhang, T., & Zhu, Z. (2018). Sakai's theorem for Q-divisors on surfaces and applications. Asian Journal of Mathematics, 22(4), 761-786. https://doi.org/10.4310/ajm.2018.v22.n4.a8

In this paper, we present a characterization of a big Q-divisor D on a smooth projective surface S with D2 > 0 and H1(OS(−D)) = 0, which generalizes a result of Sakai [Sak90] for D integral. As applications of this result for Q-divisors, we prove res... Read More about Sakai's theorem for Q-divisors on surfaces and applications.

Slope inequality for families of curves over surfaces (2017)
Journal Article
Zhang, T. (2018). Slope inequality for families of curves over surfaces. Mathematische Annalen, 371(3-4), 1095-1136. https://doi.org/10.1007/s00208-017-1551-1

In this paper, we investigate the general notion of the slope for families of curves f:X→Yf:X→Y . The main result is an answer to the above question when dimY=2dim⁡Y=2 , and we prove a lower bound for this new slope in this case over fields of any ch... Read More about Slope inequality for families of curves over surfaces.

Effective bounds of linear series on algebraic varieties and arithmetic varieties (2015)
Journal Article
Yuan, X., & Zhang, T. (2018). Effective bounds of linear series on algebraic varieties and arithmetic varieties. Journal für die reine und angewandte Mathematik, 2018(736), 255-284. https://doi.org/10.1515/crelle-2015-0025

In this paper, we prove effective upper bounds for effective sections of line bundles on projective varieties and hermitian line bundles on arithmetic varieties in terms of the volumes. They are effective versions of the Hilbert–Samuel formula and th... Read More about Effective bounds of linear series on algebraic varieties and arithmetic varieties.