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arXiv · 1512.04372

Castelnuovo-Mumford regularity and Ratliff-Rush closure

Trung Thanh Dinh·Maria Evelina Rossi·Ngo Viet Trung
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Abstract

We establish strong relationships between the Castelnuovo-Mumford regularity and the Ratliff-Rush closure of an ideal. Our results have several interesting consequences on the computation of the Ratliff-Rush closure, the stability of the Ratliff-Rush filtration, the invariance of the reduction number, and the computation of the Castelnuovo-Mumford regularity of the Rees algebra and the fiber ring. In particular, we prove that the Castelnuovo-Mumford regularity of the Rees algebra and of the fiber ring are equal for large classes of monomial ideals in two variables, thereby verifying a conjecture of Eisenbud and Ulrich for these cases.

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Trung Thanh Dinh, Maria Evelina Rossi, Ngo Viet Trung. 2015-12-14. Castelnuovo-Mumford regularity and Ratliff-Rush closure. https://arxiv.org/abs/1512.04372

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