Hodge index theorem for algebraic surfaces
= Hodge index theorem for algebraic surfaces
{c}
For a smooth projective surface and an ample divisor $A$, the <intersection pairing on the Picard group of a surface> is negative definite on the orthogonal complement of $[A]$ in $N^1(X)_{\mathbb R}$. Its signature is $(1,\rho-1)$. This is an algebraic statement valid in arbitrary characteristic, distinct from its analytic formulation for compact Kähler surfaces.