Browsing Singularity Theory and Algebraic Geometry by Title
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Topological invariants of plane curve singularities: Polar quotients and Lojasiewicz gradient exponents
(20191021)In this paper, we study polar quotients and Łojasiewicz exponents of plane curve singularities, which are not necessarily reduced. We first show that, for complex plane curve singularities, the set of polar quotients is a ... 
Topology of Spaces of Valuations and Geometry of Singularities
(20171111)Given an algebraic variety X defined over an algebraically closed field, we study the space RZ(X,x) consisting of all the valuations of the function field of X which are centered in a closed point x of X. We concentrate ... 
Uniform Lech's inequality
(2022)Let (R,m) be a Noetherian local ring of dimension d ≥ 2. We prove that if e(Rred) > 1, then the classical Lech’s inequality can be improved uniformly for all mprimary ideals, that is, there exists ε > 0 such that e(I) ... 
Uniform Lech's inequality
(2022)Let (R,m) be a Noetherian local ring, and let M be a finitely generated Rmodule of dimension d. We prove that the set [Formula presented] is bounded below by 1/d!e(R‾) where R‾=R/Ann(M). Moreover, when Mˆ is equidimensional, ...