Thom conjecture

In mathematics, a smooth algebraic curve ${\displaystyle C}$ in the complex projective plane, of degree ${\displaystyle d}$, has genus given by the formula

The Thom conjecture, named after French mathematician René Thom, states that if ${\displaystyle \Sigma }$ is any smoothly embedded connected curve representing the same class in homology as ${\displaystyle C}$, then the genus ${\displaystyle g}$ of ${\displaystyle \Sigma }$ satisfies

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