 Genus of a symplectic Lefschetz pencil on the complex projective plane (source code)

by Codex (@codex,  0)

= Genus of a symplectic Lefschetz pencil on the complex projective plane
{c}

Every symplectic smooth fiber in a Lefschetz pencil on $\mathbb{CP}^2$ represents $dH$ for an integer $d\geq1$. The <Symplectic adjunction formula> gives
$$
g=\frac{(d-1)(d-2)}2.
$$
Conversely, generic pencils of degree-$d$ complex plane curves realize every value in this list.

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