Kähler-Ricci Tangent Flows are Infinitesimally Algebraic
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914803594821632 |
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| author | Hallgren, Max |
| author_facet | Hallgren, Max |
| contents | We show that any tangent cone of a singular shrinking Kähler-Ricci soliton is a normal affine algebraic variety. Moreover, the regular set of such a tangent cone in the metric sense coincides with the regular set in the algebraic sense. Along the way, we give a parabolic proof of Hörmander's $L^{2}$ estimate, which can be used to solve the $\overline{\partial}$-equation on any singular shrinking Kähler-Ricci soliton. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_06577 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Kähler-Ricci Tangent Flows are Infinitesimally Algebraic Hallgren, Max Differential Geometry We show that any tangent cone of a singular shrinking Kähler-Ricci soliton is a normal affine algebraic variety. Moreover, the regular set of such a tangent cone in the metric sense coincides with the regular set in the algebraic sense. Along the way, we give a parabolic proof of Hörmander's $L^{2}$ estimate, which can be used to solve the $\overline{\partial}$-equation on any singular shrinking Kähler-Ricci soliton. |
| title | Kähler-Ricci Tangent Flows are Infinitesimally Algebraic |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2312.06577 |