Computing The Invariants of Intersection Algebras of Principal Monomial Ideals
Abstract
We continue the study of intersection algebras $\mathcal B = \mathcal B_R(I, J)$ of two ideals $I, J$ in a commutative Noetherian ring $R$. In particular, we exploit the semigroup ring and toric structures in order to calculate various invariants of the intersection algebra when $R$ is a polynomial ring over a field and $I,J$ are principal monomial ideals. Specifically, we calculate the $F$-signature, divisor class group, and Hilbert-Samuel and Hilbert-Kunz multiplicities, sometimes restricting to certain cases in order to obtain explicit formulæ. This provides a new class of rings where formulæ for the $F$-signature and Hilbert-Kunz multiplicity, dependent on families of parameters, are provided.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2018
- DOI:
- 10.48550/arXiv.1810.01499
- arXiv:
- arXiv:1810.01499
- Bibcode:
- 2018arXiv181001499E
- Keywords:
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- Mathematics - Commutative Algebra;
- 13A15;
- 05E40;
- 20M25