Turkish Journal of Mathematics
DOI
10.3906/mat-1912-111
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
First Page
1510
Last Page
1519
Recommended Citation
LI, JINJIA
(2020)
"Asymptotic socle behaviors for cones over curves in positive characteristic,"
Turkish Journal of Mathematics: Vol. 44:
No.
4, Article 31.
https://doi.org/10.3906/mat-1912-111
Available at:
https://journals.tubitak.gov.tr/math/vol44/iss4/31
