Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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REALIZING A FAKE PROJECTIVE PLANE AS A DEGREE 25 SURFACE IN ℙ5

  • Lev Borisov (Hill Center Department of Mathematics Rutgers University) ;
  • Zachary Lihn (Department of Mathematics Columbia University)
  • Received : 2023.03.21
  • Accepted : 2024.04.05
  • Published : 2024.07.01
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Abstract

Fake projective planes are smooth complex surfaces of general type with Betti numbers equal to that of the usual projective plane. Recent explicit constructions of fake projective planes embed them via their bicanonical embedding in ℙ9. In this paper, we study Keum's fake projective plane (a = 7, p = 2, {7}, D327) and use the equations of [1] to construct an embedding of fake projective plane in ℙ5. We also simplify the 84 cubic equations defining the fake projective plane in ℙ9.

Keywords

Acknowledgement

The authors thank the DIMACS REU program at Rutgers University for supporting this research project. This work was carried out while the second author was supported by NSF grant CCF-1852215.

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