【报告摘要】Recently, Ein-Ha-Lazarsfeld proved that if I is a homogeneous ideal whose zero locus is a non-singular complex projective scheme, then the saturation degree sdeg(I^n) is bounded above by a linear function of n whose slope is less or equal the maximal generating degree of I. Inspired by the asymptotic behavior of the Castelnuovo-Mumford regularity, we show that for an arbitrary graded ideal I in an arbitrary graded ring, sdeg(I^n) is either a constant or a linear function for n large enough whose slope is one of the generating degrees of I.

【报告人简介】Prof. Ngo Viet Trung graduated from the Martin-Luther University in Halle in 1978. He was elected Fellow of the Third World Academy of Sciences in 2000, Director of the Institute of Mathematics of Vietnam Academy of Science and Technology in 2006-2013, and President of the Vietnam Mathematical Society 2018-2023.