Thom conjecture
In mathematics, a smooth algebraic curve C {\displaystyle C} in the complex projective plane, of degree d {\displaystyle d} , has genus given by the genus–degree formula g = ( d − 1 ) ( d − 2 ) / 2 {\displaystyle g=(d-1)(d-2)/2} . The Thom conjecture, named after French mathematician René Thom, states that if Σ {\displaystyle \Sigma } is any smoothly embedded connected curve representing the same class in homology as C {\displaystyle C} , then the genus g {\displaystyle g} of Σ {\displaystyle \Sigma } satisfies the inequality g ≥ ( d − 1 ) ( d − 2 ) / 2 {\displaystyle g\geq (d-1)(d-2)/2} .