𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Hilbert–Kunz Functions of Cubic Curves and Surfaces

✍ Scribed by Ragnar-Olaf Buchweitz; Qun Chen

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
293 KB
Volume
197
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

We determine the Hilbert᎐Kunz function of plane elliptic curves in odd characteristic, as well as over arbitrary fields the generalized Hilbert᎐Kunz functions of nodal cubic curves. Together with results of K. Pardue and P. Monsky, this completes the list of Hilbert᎐Kunz functions of plane cubics. Combining these Ž . results with the calculation of the generalized Hilbert᎐Kunz function of Cayley's cubic surface, it follows that in each degree and over any field of positive characteristic there are curves resp. surfaces taking on the minimally possible Hilbert᎐Kunz multiplicity.

📜 SIMILAR VOLUMES

On the Hilbert Function of Fat Points on
On the Hilbert Function of Fat Points on a Rational Normal Cubic
✍ Maria Virginia Catalisano; Alessandro Gimigliano 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 238 KB

In this paper we find an algorithm which computes the Hilbert function of schemes Z of ''fat points'' in ‫ސ‬ 3 whose support lies on a rational normal cubic curve C. The algorithm shows that the maximality of the Hilbert function in degree Ž t is related to the existence of fixed curves either C its