A direct limit for limit Hilbert-Kunz multiplicity for smooth projective curves

Autor(en): Brenner, Holger 
Li, Jinjia
Miller, Claudia
Stichwörter: Harder-Narasimhan filtrations; Hilbert-Kunz multiplicity; IDEALS; Mathematics; SEMISTABILITY
Erscheinungsdatum: 2012
Herausgeber: ACADEMIC PRESS INC ELSEVIER SCIENCE
Journal: JOURNAL OF ALGEBRA
Volumen: 372
Startseite: 488
Seitenende: 504
Zusammenfassung: 
This paper concerns the question of whether a more direct limit can be used to obtain the limit Hilbert-Kunz multiplicity, a possible candidate for a characteristic zero Hilbert-Kunz multiplicity. The main goal is to establish an affirmative answer for one of the main cases for which the limit Hilbert-Kunz multiplicity is even known to exist, namely that of graded ideals in the homogeneous coordinate ring of smooth projective curves. The proof involves more careful estimates of bounds found independently by Brenner and Trivedi on the dimensions of the cohomologies of twists of the syzygy bundle as the characteristic p goes to infinity and uses asymptotic results of Trivedi on the slopes of Harder-Narasimham filtrations of Frobenius pullbacks of bundles. In view of unpublished results of Gessel and Monsky, the case of maximal ideals in diagonal hypersurfaces is also discussed in depth. (c) 2012 Elsevier Inc. All rights reserved.
ISSN: 00218693
DOI: 10.1016/j.jalgebra.2012.10.004

Show full item record

Page view(s)

4
Last Week
0
Last month
2
checked on Feb 27, 2024

Google ScholarTM

Check

Altmetric