Stable $2$-systoles, scalar curvature and spin$^c$ comass bounds
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918472134426624 |
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| author | Cecchini, Simone Hirsch, Sven Zeidler, Rudolf |
| author_facet | Cecchini, Simone Hirsch, Sven Zeidler, Rudolf |
| contents | We prove a sharp stable $2$-systolic inequality for complex projective space under the scalar curvature lower bound of the normalized Fubini-Study metric. If $M$ is diffeomorphic to $\mathbb{C}\mathrm{P}^n$ and $\mathrm{scal}_g\ge 4n(n+1)$, then $\mathrm{sys}_2^{\mathrm{st}}(M,g)\le π$. Moreover, equality holds only for the Fubini-Study metric, up to biholomorphism after choosing the corresponding complex structure. The proof uses Spin$^c$ Dirac operators, a comass estimate for the curvature term in the Lichnerowicz formula, and stable norm-comass duality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25900 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stable $2$-systoles, scalar curvature and spin$^c$ comass bounds Cecchini, Simone Hirsch, Sven Zeidler, Rudolf Differential Geometry 53C24, 53C27 (Primary), 53C21, 53C23, 53C38, 58J20, 32Q20 (Secondary) We prove a sharp stable $2$-systolic inequality for complex projective space under the scalar curvature lower bound of the normalized Fubini-Study metric. If $M$ is diffeomorphic to $\mathbb{C}\mathrm{P}^n$ and $\mathrm{scal}_g\ge 4n(n+1)$, then $\mathrm{sys}_2^{\mathrm{st}}(M,g)\le π$. Moreover, equality holds only for the Fubini-Study metric, up to biholomorphism after choosing the corresponding complex structure. The proof uses Spin$^c$ Dirac operators, a comass estimate for the curvature term in the Lichnerowicz formula, and stable norm-comass duality. |
| title | Stable $2$-systoles, scalar curvature and spin$^c$ comass bounds |
| topic | Differential Geometry 53C24, 53C27 (Primary), 53C21, 53C23, 53C38, 58J20, 32Q20 (Secondary) |
| url | https://arxiv.org/abs/2604.25900 |