Abstract
Let R be a Cohen–Macaulay local domain. In this paper we study the cone of Cohen–Macaulay modules inside the Grothendieck group of finitely generated R-modules modulo numerical equivalences, introduced in Chan and Kurano (The cone spanned by maximal Cohen–Macaulay modules and an application. Trans Am Math Soc, to appear, 2015). We prove a result about the boundary of this cone for Cohen–Macaulay domain admitting de Jong’s alterations, and use it to derive some corollaries on finiteness of isomorphism classes of maximal Cohen–Macaulay ideals. Finally, we explicitly compute the Cohen–Macaulay cone for certain isolated hypersurface singularities defined by \(\xi \eta - f(x_1, \ldots , x_n)\).
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H. Dao is partially supported by NSF Grant DMS 1104017. K. Kurano is partially supported by JSPS KAKENHI Grant 24540054.
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Dao, H., Kurano, K. Boundary and shape of Cohen–Macaulay cone. Math. Ann. 364, 713–736 (2016). https://doi.org/10.1007/s00208-015-1231-y
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DOI: https://doi.org/10.1007/s00208-015-1231-y