In this paper, the author extends Peter Li and Tian Gang’s results on the heat kernel from projective varieties to analytic varieties. The author gets an upper bound of the heat kernel on analytic varieties and prove...In this paper, the author extends Peter Li and Tian Gang’s results on the heat kernel from projective varieties to analytic varieties. The author gets an upper bound of the heat kernel on analytic varieties and proves several properties. Moreover, the results are extended to vector bundles. The author also gets an upper bound of the heat operators of some Schrondinger type operators on vector bundles. As a corollary, an upper bound of the trace of the heat operators is obtained.展开更多
In this paper,we give a suficient condition under which an involution monoid generates a variety with continuum many subvarieties.According to this result,several involution J-trivial monoids are shown to generate var...In this paper,we give a suficient condition under which an involution monoid generates a variety with continuum many subvarieties.According to this result,several involution J-trivial monoids are shown to generate varieties with continuum many subvarieties.These examples include Rees quotients of free involution monoids,Lee monoids with involution,and Straubing monoids with involution.展开更多
Some theorems concerning the projective normality and extrinsic geometry on the smooth variety are proved under some supposed conditions related to the arithmetic genus of the smooth variety.
Let X C P^NC be an n-dimensional nondegenerate smooth projective variety containing an mdimensional subvariety Y.Assume that either m〉n/2 and X is a complete intersection or that m≥ N2.We show deg（X）｜deg（Y）and ...Let X C P^NC be an n-dimensional nondegenerate smooth projective variety containing an mdimensional subvariety Y.Assume that either m〉n/2 and X is a complete intersection or that m≥ N2.We show deg（X）｜deg（Y）and codim Y Y ≥codimPN X,where Y is the linear span of Y.These bounds are sharp.As an application,we classify smooth projective n-dimensional quadratic varieties swept out by m≥[n/2]＋1 dimensional quadrics passing through one point.展开更多
文摘In this paper, the author extends Peter Li and Tian Gang’s results on the heat kernel from projective varieties to analytic varieties. The author gets an upper bound of the heat kernel on analytic varieties and proves several properties. Moreover, the results are extended to vector bundles. The author also gets an upper bound of the heat operators of some Schrondinger type operators on vector bundles. As a corollary, an upper bound of the trace of the heat operators is obtained.
基金supported by the National Natural Science Foundation of China(Nos.12271224,12171213,11771191)the Fundamental Research Funds for the Central Universities(No.lzujbky-2023-ey06)the Natural Science Foundation of Gansu Province(No.20JR5RA275).
文摘In this paper,we give a suficient condition under which an involution monoid generates a variety with continuum many subvarieties.According to this result,several involution J-trivial monoids are shown to generate varieties with continuum many subvarieties.These examples include Rees quotients of free involution monoids,Lee monoids with involution,and Straubing monoids with involution.
文摘Some theorems concerning the projective normality and extrinsic geometry on the smooth variety are proved under some supposed conditions related to the arithmetic genus of the smooth variety.
文摘Let X C P^NC be an n-dimensional nondegenerate smooth projective variety containing an mdimensional subvariety Y.Assume that either m〉n/2 and X is a complete intersection or that m≥ N2.We show deg（X）｜deg（Y）and codim Y Y ≥codimPN X,where Y is the linear span of Y.These bounds are sharp.As an application,we classify smooth projective n-dimensional quadratic varieties swept out by m≥[n/2]＋1 dimensional quadrics passing through one point.
