The main purpose of this paper is to introduce the matrix extension of the pseudo Laguerre matrix polynomials and to explore the formal properties of the operational rules and the principle of quasi-monomiality to der...The main purpose of this paper is to introduce the matrix extension of the pseudo Laguerre matrix polynomials and to explore the formal properties of the operational rules and the principle of quasi-monomiality to derive a number of properties for pseudo Laguerre matrix polynomials.展开更多
Given a klt singularity x∈(X,D),we show that a quasi-monomial valuation v with a finitely generated associated graded ring is a minimizer of the normalized vol-ume function vol_((X,D),x),if and only if v induces a de...Given a klt singularity x∈(X,D),we show that a quasi-monomial valuation v with a finitely generated associated graded ring is a minimizer of the normalized vol-ume function vol_((X,D),x),if and only if v induces a degeneration to a K-semistable log Fano cone singularity.Moreover,such a minimizer is unique among all quasi-mono-mial valuations up to rescaling.As a consequence,we prove that for a klt singular-ity x∈X on the Gromov-Hausdorff limit of Kähler-Einstein Fano manifolds,the intermediate K-semistable cone associated with its metric tangent cone is uniquely determined by the algebraic structure of x∈X,hence confirming a conjecture by Donaldson-Sun.展开更多
文摘The main purpose of this paper is to introduce the matrix extension of the pseudo Laguerre matrix polynomials and to explore the formal properties of the operational rules and the principle of quasi-monomiality to derive a number of properties for pseudo Laguerre matrix polynomials.
文摘Given a klt singularity x∈(X,D),we show that a quasi-monomial valuation v with a finitely generated associated graded ring is a minimizer of the normalized vol-ume function vol_((X,D),x),if and only if v induces a degeneration to a K-semistable log Fano cone singularity.Moreover,such a minimizer is unique among all quasi-mono-mial valuations up to rescaling.As a consequence,we prove that for a klt singular-ity x∈X on the Gromov-Hausdorff limit of Kähler-Einstein Fano manifolds,the intermediate K-semistable cone associated with its metric tangent cone is uniquely determined by the algebraic structure of x∈X,hence confirming a conjecture by Donaldson-Sun.
