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Armando j18eos
Armando j18eos
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Since $X$ admits a Kähler-Einstein metric [Theorem 2,3] and [Theorem 1,2], if $K_X$ is ample the inequality holds with $H=K_X$, by [Theorem IV.4.16,1] the inequality holds.

[1] S. Kobayashi (1987) Differential Geometry of Complex Vector Bundles, Iwanami Shoten Publishers and Princeton University Press.

[2] S.-T. Yau - Calabi's conjecture and some new results in algebraic geometry, Proc. Nat. Acad. Sci. 74 (1977) 1798-1799.

[3] S.-T. Yau - On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation. I, Comm. Pure Appl. Math. 31 (1978) 339-411.

Since $X$ admits a Kähler-Einstein metric [Theorem 2,3] and [Theorem 1,2], by [Theorem IV.4.16,1] the inequality holds.

[1] S. Kobayashi (1987) Differential Geometry of Complex Vector Bundles, Iwanami Shoten Publishers and Princeton University Press.

[2] S.-T. Yau - Calabi's conjecture and some new results in algebraic geometry, Proc. Nat. Acad. Sci. 74 (1977) 1798-1799.

[3] S.-T. Yau - On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation. I, Comm. Pure Appl. Math. 31 (1978) 339-411.

Since $X$ admits a Kähler-Einstein metric [Theorem 2,3] and [Theorem 1,2], if $K_X$ is ample the inequality holds with $H=K_X$, by [Theorem IV.4.16,1].

[1] S. Kobayashi (1987) Differential Geometry of Complex Vector Bundles, Iwanami Shoten Publishers and Princeton University Press.

[2] S.-T. Yau - Calabi's conjecture and some new results in algebraic geometry, Proc. Nat. Acad. Sci. 74 (1977) 1798-1799.

[3] S.-T. Yau - On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation. I, Comm. Pure Appl. Math. 31 (1978) 339-411.

Source Link
Armando j18eos
Armando j18eos
  • 828
  • 1
  • 7
  • 22

Since $X$ admits a Kähler-Einstein metric [Theorem 2,3] and [Theorem 1,2], by [Theorem IV.4.16,1] the inequality holds.

[1] S. Kobayashi (1987) Differential Geometry of Complex Vector Bundles, Iwanami Shoten Publishers and Princeton University Press.

[2] S.-T. Yau - Calabi's conjecture and some new results in algebraic geometry, Proc. Nat. Acad. Sci. 74 (1977) 1798-1799.

[3] S.-T. Yau - On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation. I, Comm. Pure Appl. Math. 31 (1978) 339-411.