The Genus of Embedded Surfaces in the Projective Plane

  title={The Genus of Embedded Surfaces in the Projective Plane},
  author={Peter B. Kronheimer and Tomasz S. Mrowka},
  journal={Mathematical Research Letters},
1. Statement of the result The genus of a smooth algebraic curve of degree d in CP is given by the formula g = (d − 1)(d − 2)/2. A conjecture sometimes attributed to Thom states that the genus of the algebraic curve is a lower bound for the genus of any smooth 2-manifold representing the same homology class. The conjecture has previously been proved for d ≤ 4 and for d = 6, and less sharp lower bounds for the genus are known for all degrees [5,6,7,10,14]. In this note we confirm the conjecture… Expand
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