Corollary 15.30.4`8C4A9CEF04C8`

Corollary 15.30.4.8C4A9CEF04C8 Let $X_0$ be the elliptic threefold of theorem 12.19.1, with the balanced metric $\omega $ of proposition 12.19.18. On $X_0\times \mathbb P^2$, with background $H=\omega +\kappa $, the densities $f=Rq_\alpha $ of the preceding theorem satisfy

\[ v_-(H)=0,\qquad b_ H(f)=240\pi , \qquad \mathrm{MA}^{\mathrm{ext}}_ H(u_\alpha )=240\pi f\, \mathrm{d}V. \]

Proof. Theorem 12.19.1 gives $v_-(\omega )=0$, and proposition 12.19.18 gives $V_0=24\pi $. The product theorem applies with $m=3$, $k=2$ and $C=\binom 53=10$. $\square$

Cite this page

BibTeX citation

@misc{pome-tag-8C4A9CEF04C8,
  author = {{Pome contributors}},
  title = {Corollary 15.30.4},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/8C4A9CEF04C8/}
}

Comments

Corrections, questions, and mathematical discussion are welcome. Sign in with GitHub to comment. Comments are public.

Read this page’s discussion on GitHub Post a comment on GitHub

Corollary 15.30.48C4A9CEF04C8

Comments

Corollary 15.30.4`8C4A9CEF04C8`