The extension of numerically trivial divisors on a family

Algebraic Geometry Seminar

Organizers：

Caucher Birkar，贾甲

Speaker：

Lingyao Xie University of California San Diego

Time：

Fri., 09:00-10:00 am, Oct. 31, 2025

Online：

Zoom Meeting ID: 262 865 5007

Passcode: YMSC

Title:

The extension of numerically trivial divisors on a family

Abstract:

For a projective morphism f:X to S, we explore when it is possible to extend a divisor that is numerically trivial over an open subset to a global relativelu num-trivial divisor. In particular, we show that such L alwasy exists after a semi-stable reduction when dim S=1.On the other hand, we give an example showing that L may not exts if dim S >1, which also gives an f_U nef divisor M_U shat canno extend to an f-nef divisor M for any compactification of f|_U, even after replacing X_U with any higher birational model.