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In the case of surfaces the inequality is always true EDIT: with the only exception of surfaces ruled over a curve of genus $>1$. It has beeen proven by Miyaoka [On the Chern numbers of surfaces of general type. Invent. Math. 42 (1977), 225–237] for surfaces of general type. For surfaces not of general type it can be proven easily by looking at the classification.

In the case of surfaces the inequality is always true. It has beeen proven by Miyaoka [On the Chern numbers of surfaces of general type. Invent. Math. 42 (1977), 225–237] for surfaces of general type. For surfaces not of general type it can be proven easily by looking at the classification.

In the case of surfaces the inequality is true EDIT: with the only exception of surfaces ruled over a curve of genus $>1$. It has beeen proven by Miyaoka [On the Chern numbers of surfaces of general type. Invent. Math. 42 (1977), 225–237] for surfaces of general type. For surfaces not of general type it can be proven easily by looking at the classification.

Source Link
rita
rita
  • 6.3k
  • 1
  • 29
  • 39

In the case of surfaces the inequality is always true. It has beeen proven by Miyaoka [On the Chern numbers of surfaces of general type. Invent. Math. 42 (1977), 225–237] for surfaces of general type. For surfaces not of general type it can be proven easily by looking at the classification.