论文标题
关于单一理想不变链的规律性和投影维度
On regularity and projective dimension of invariant chains of monomial ideals
论文作者
论文摘要
最近已经广泛研究了在功能越来越大的功能的作用下，无限多项式环的理想是不变的。特别令人感兴趣的是在有限维多项式子环中这种理想的截断的渐近行为。人们已经猜想Castelnuovo- -Mumford的规律性和投影维度最终是沿此类截断的线性功能。在本文中，我们提供了这些猜想的证据。我们表明，对于单一理想，投影维度最终是线性的，而规律性是渐近线性的。
Ideals in infinite-dimensional polynomial rings that are invariant under the action of the monoid of increasing functions have been extensively studied recently. Of particular interest is the asymptotic behavior of truncations of such an ideal in finite-dimensional polynomial subrings. It has been conjectured that the Castelnuovo--Mumford regularity and projective dimension are eventual linear functions along such truncations. In the present paper we provide evidence for these conjectures. We show that for monomial ideals the projective dimension is eventually linear, while the regularity is asymptotically linear.
