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| On the positivity of high-degree Schur classes of an ample vector bundle | |
| 作者姓名： | Jian Xiao |
| 作者单位： | Department of Mathematical Sciences and Yau Mathematical Sciences Center |
| 基金项目： | supported by Tsinghua University Initiative Scientific Research Program(Grant No.2019Z07L02016);National Natural Science Foundation of China(Grant No.11901336)。 |
| 摘 要： | 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. |
| 关 键 词： | ample vector bundles Griffiths conjecture positive polynomials Schur classes |
On the positivity of high-degree Schur classes of an ample vector bundle |
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| Jian Xiao.On the positivity of high-degree Schur classes of an ample vector bundle[J].中国科学 数学(英文版),2022,65(1):51-62. | |
| Authors: | Xiao Jian |
| Institution: | 1.Department of Mathematical Sciences and Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China ; |
| Abstract: | 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. |
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