Chern Classes of Open Projected Richardson Varieties and of Affine Schubert Cells
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908590187479040 |
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| author | Fan, Neil J. Y. Guo, Peter L. Su, Changjian Xiong, Rui |
| author_facet | Fan, Neil J. Y. Guo, Peter L. Su, Changjian Xiong, Rui |
| contents | The open projected Richardson varieties form a stratification for the partial flag variety $G/P$. We compare the Segre--MacPherson classes of open projected Richardson varieties with those of the corresponding affine Schubert cells by pushing or pulling these classes to the affine Grassmannian. In the case of the Grassmannian $G/P=\operatorname{Gr}_k(\mathbb{C}^n)$, the open projected Richardson varieties are known as open positroid varieties. We obtain symmetric functions that represent the Segre--MacPherson classes of these open positroid varieties, constructed explicitly in terms of pipe dreams for affine permutations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16172 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chern Classes of Open Projected Richardson Varieties and of Affine Schubert Cells Fan, Neil J. Y. Guo, Peter L. Su, Changjian Xiong, Rui Algebraic Geometry Combinatorics The open projected Richardson varieties form a stratification for the partial flag variety $G/P$. We compare the Segre--MacPherson classes of open projected Richardson varieties with those of the corresponding affine Schubert cells by pushing or pulling these classes to the affine Grassmannian. In the case of the Grassmannian $G/P=\operatorname{Gr}_k(\mathbb{C}^n)$, the open projected Richardson varieties are known as open positroid varieties. We obtain symmetric functions that represent the Segre--MacPherson classes of these open positroid varieties, constructed explicitly in terms of pipe dreams for affine permutations. |
| title | Chern Classes of Open Projected Richardson Varieties and of Affine Schubert Cells |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2501.16172 |