Geometric regularity of powers of two-dimensional squarefree monomial ideals
Abstract
Let $I$ be a two-dimensional squarefree monomial ideal of a polynomial ring $S$. We evaluate the geometric regularity, $a_i$-invariants for $i\geq 1$ of the power $I^n$. It turns out they are all linear functions in $n$ from $n=2$. Moreover, it is proved $\mbox{g-reg}(S/I^n)=\reg(S/I^{(n)})$ for all $n\geq 1$.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2018
- DOI:
- 10.48550/arXiv.1808.07266
- arXiv:
- arXiv:1808.07266
- Bibcode:
- 2018arXiv180807266L
- Keywords:
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- Mathematics - Commutative Algebra;
- 13D45 (Primary);
- 13C99 (Secondary)
- E-Print:
- 23 pages to appear in JACO