اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدLinear flags and Koszul filtrations
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We show that the graded maximal ideal of a graded $K$-algebra $R$ has linear quotients for a suitable choice and order of its generators if the defining ideal of $R$ has a quadratic Grobner basis with respect to the reverse lexicographic order, and show that this linear quotient property for algebras defined by binomial edge ideals characterizes closed graphs. Furthermore, for algebras defined by binomial edge ideals attached to a closed graph and for join-meet rings attached to a finite distributive lattice we present explicit Koszul filtrations.
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This is a survey paper on commutative Koszul algebras and Castelnuovo-Mumford regularity. We describe several techniques to establish the Koszulness of algebras. We discuss variants of the Koszul property such as strongly Koszul, absolutely Koszul an
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an R-module. The first part of the notes is devoted to the introduction of Koszul algebras and their characterization in terms of Castelnuovo-Mumford regularity. In the second part we discuss recernt results on the syzygies of Koszul algebras. Finally in the last part we discuss the Koszul property of Veronese algebras and of algebras associated with collections of hyperspaces.
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polynomial whose coefficients give the mixed multiplicities. This polynomial exists if and only if the dimension of the nilradical of the completion of $R$ is less than the dimension of $R$, which holds for instance if $R$ is excellent and reduced. We show that many of the classical theorems for mixed multiplicities of $m_R$-primary ideals hold for filtrations, including the famous Minkowski inequalities of Teissier, and Rees and Sharp.
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