The positivity (nefness, strict nefness, ampleness) of divisors plays an important role in birational geometry. It is well-known that strictly nef divisors are not necessarily ample. However, Serrano's conjecture predicts that a small deformation of a strictly nef divisor in the direction of the canonical divisor is ample. In this talk, I will survey some recent progress on this conjecture. Part of my works are joint with Roberto Svaldi, Part of them are joint with Shin-ichi Matsumura.
Haidong Liu is currently an associate professor at Sun Yat-sen University. He obtained his Ph.D. at Kyoto University in 2018 under the supervision of Osamu Fujino. His research focuses on the minimal model program and related topics.
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