Minimal free resolutions for certain affine monomial curve
Abstract
Given an arbitrary field k and an arithmetic sequence of positive integers m_0<...<m_n, we consider the affine monomial curve parameterized by X_0=t^{m_0},...,X_n=t^{m_n}. In this paper, we conjecture that the Betti numbers of its coordinate ring are completely determined by n and the value of m_0 modulo n. We first show that the defining ideal of the monomial curve can be written as a sum of two determinantal ideals. Using this fact, we describe the minimal free resolution of the coordinate ring in the following three cases: when m_0 is 1 modulo n (determinantal), when m_0 is n modulo n (almost determinantal), and when m_0 is 2 modulo n and n=4 (Gorenstein of codimension 4).
Cite
@article{arxiv.1011.4247,
title = {Minimal free resolutions for certain affine monomial curve},
author = {Philippe Gimenez and Indranath Sengupta and Hema Srinivasan},
journal= {arXiv preprint arXiv:1011.4247},
year = {2012}
}
Comments
9 pages. To appear in 'Commutative Algebra and its Connections to Geometry (PASI 2009)', Contemporary Mathematics, AMS