Asymptotic behaviour of the saturation degree

Thời gian: 14:00 đến 16:00 Ngày 08/10/2024

Địa điểm: Phòng C101, VIASM, 157 phố Chùa Láng, Hà Nội

Báo cáo viên: Prof. Ngô Việt Trung, Viện Toán học, Viện Hàn lâm Khoa hoc và Công nghệ Việt Nam

Tóm tắt: 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.