- Turkish Journal of Mathematics
- Vol: 44 Issue: 4
- Asymptotic socle behaviors for cones over curves in positive characteristic
Asymptotic socle behaviors for cones over curves in positive characteristic
Authors : Jınjıa Li
Pages : 1510-1519
Doi:10.3906/mat-1912-111
View : 7 | Download : 0
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :This paper studies the distribution of socle degrees of $R/I^{[p^e]}$ when $e$ is large, for a homogeneous ideal $I$ in a two-dimensional standard-graded normal domain $R$ in positive characteristic $p$. We prove that the distribution is very much related to the asymptotic slopes of the syzygy bundle Syz$ I $, which have been known to determine the Hilbert-Kunz multiplicity of $I$.Keywords : Frobenius power, socle, diagonal $F$-threshold, semistability, strong semistability, syzygy bundle, Hilbert-Kunz multiplicity