arXiv
Open Access
2017
Mapping properties of the Hilbert and Fubini--Study maps in Kähler geometry
Yoshinori Hashimoto
Abstrak
Suppose that we have a compact Kähler manifold $X$ with a very ample line bundle $\mathcal{L}$. We prove that any positive definite hermitian form on the space $H^0 (X,\mathcal{L})$ of holomorphic sections can be written as an $L^2$-inner product with respect to an appropriate hermitian metric on $\mathcal{L}$. We apply this result to show that the Fubini--Study map, which associates a hermitian metric on $\mathcal{L}$ to a hermitian form on $H^0 (X,\mathcal{L})$, is injective.
Topik & Kata Kunci
Penulis (1)
Y
Yoshinori Hashimoto
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2017
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓