We prove that some holomorphic functions on the moduli space of tori have only simple zeros.Instead of computing the derivative with respect to the moduli parameter τ, we introduce a conceptual proof by applying Pain...We prove that some holomorphic functions on the moduli space of tori have only simple zeros.Instead of computing the derivative with respect to the moduli parameter τ, we introduce a conceptual proof by applying Painlevé Ⅵ equation. As an application of this simple zero property, we obtain the smoothness of the degeneracy curves of trivial critical points for some multiple Green function.展开更多
Let X be a smooth projective variety of dimension n,and let E be an ample vector bundle over X.We show that any Schur class of E,lying in the cohomology group of bidegree(n-1,n-1),has a representative which is strictl...Let X be a smooth projective variety of dimension n,and let E be an ample vector bundle over X.We show that any Schur class of E,lying in the cohomology group of bidegree(n-1,n-1),has a representative which is strictly positive in the sense of smooth forms.This conforms the prediction of Griffiths conjecture on the positive polynomials of Chern classes/forms of an ample vector bundle on the form level,and thus strengthens the celebrated positivity results of Fulton and Lazarsfeld(1983)for certain degrees.展开更多
Motivated by our previous work on Hodge-index type theorems, we give a form of mixed HodgeRiemann bilinear relation by using the notion of m-positivity, whose proof is an adaptation of the works of Timorin(1998) and D...Motivated by our previous work on Hodge-index type theorems, we give a form of mixed HodgeRiemann bilinear relation by using the notion of m-positivity, whose proof is an adaptation of the works of Timorin(1998) and Dinh and Nguyen(2006). This mixed Hodge-Riemann bilinear relation holds with respect to mixed polarizations in which some satisfy particular positivity condition, but could be degenerate along some directions. In particular, it applies to fibrations of compact Kahler manifolds.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 11701312)
文摘We prove that some holomorphic functions on the moduli space of tori have only simple zeros.Instead of computing the derivative with respect to the moduli parameter τ, we introduce a conceptual proof by applying Painlevé Ⅵ equation. As an application of this simple zero property, we obtain the smoothness of the degeneracy curves of trivial critical points for some multiple Green function.
基金supported by Tsinghua University Initiative Scientific Research Program(Grant No.2019Z07L02016)National Natural Science Foundation of China(Grant No.11901336)。
文摘Let X be a smooth projective variety of dimension n,and let E be an ample vector bundle over X.We show that any Schur class of E,lying in the cohomology group of bidegree(n-1,n-1),has a representative which is strictly positive in the sense of smooth forms.This conforms the prediction of Griffiths conjecture on the positive polynomials of Chern classes/forms of an ample vector bundle on the form level,and thus strengthens the celebrated positivity results of Fulton and Lazarsfeld(1983)for certain degrees.
基金supported by Tsinghua University Initiative Scientific Research Program (Grant No. 2019Z07L02016)National Natural Science Foundation of China (Grant No. 11901336)。
文摘Motivated by our previous work on Hodge-index type theorems, we give a form of mixed HodgeRiemann bilinear relation by using the notion of m-positivity, whose proof is an adaptation of the works of Timorin(1998) and Dinh and Nguyen(2006). This mixed Hodge-Riemann bilinear relation holds with respect to mixed polarizations in which some satisfy particular positivity condition, but could be degenerate along some directions. In particular, it applies to fibrations of compact Kahler manifolds.
