This paper is the sequel to our study of heat kernel on Ricci shrinkers[29].In this paper,we improve many estimates in[29]and extend the recent progress of Bamler[2].In particular,we drop the compactness and curvature...This paper is the sequel to our study of heat kernel on Ricci shrinkers[29].In this paper,we improve many estimates in[29]and extend the recent progress of Bamler[2].In particular,we drop the compactness and curvature boundedness assumptions and show that the theory of F-convergence holds naturally on any Ricci flows induced by Ricci shrinkers.展开更多
Let X be a complex smooth quasi-projective variety with a fixed epimorphism ν:π_(1)(X)■H,where H is a finitely generated abelian group with rank H≥1.In this paper,the authors study the asymptotic behaviour of Bett...Let X be a complex smooth quasi-projective variety with a fixed epimorphism ν:π_(1)(X)■H,where H is a finitely generated abelian group with rank H≥1.In this paper,the authors study the asymptotic behaviour of Betti numbers with all possible field coefficients and the order of the torsion subgroup of singular homology associated toν,known as the L^(2)-type invariants.When ν is orbifold effective,explicit formulas of these invariants at degree 1 are give.This generalizes the authors’previous work for H≌Z.展开更多
基金supported by the YSBR-001,the NSFC(12201597)research funds from USTC(University of Science and Technology of China)and CAS(Chinese Academy of Sciences)+2 种基金supported by the YSBR-001the NSFC(11971452,12026251)a research fund from USTC.
文摘This paper is the sequel to our study of heat kernel on Ricci shrinkers[29].In this paper,we improve many estimates in[29]and extend the recent progress of Bamler[2].In particular,we drop the compactness and curvature boundedness assumptions and show that the theory of F-convergence holds naturally on any Ricci flows induced by Ricci shrinkers.
基金supported by the National Key Research and Development Project(No.SQ2020YFA070080)the National Natural Science Foundation of China(No.12001511)+1 种基金the Project of Stable Support for Youth Team in Basic Research Field CAS(No.YSBR-001)the Project of Analysis and Geometry on Bundles of the Ministry of Science and Technology of China and the Fundamental Research Funds for the Central Universities。
文摘Let X be a complex smooth quasi-projective variety with a fixed epimorphism ν:π_(1)(X)■H,where H is a finitely generated abelian group with rank H≥1.In this paper,the authors study the asymptotic behaviour of Betti numbers with all possible field coefficients and the order of the torsion subgroup of singular homology associated toν,known as the L^(2)-type invariants.When ν is orbifold effective,explicit formulas of these invariants at degree 1 are give.This generalizes the authors’previous work for H≌Z.
