- Simplifying explicit equations of fake projective planes
- Project Year:
2023
- REU Student (s):
Mattie Ji | Brown University RI
- Student 1 Institution:
Brown University
- Project Mentor:
Lev Borisov
- Project Mentor Area:
Mathematics
- Project Abstract:
A fake projective plane is a complex surface with the same Betti numbers as CP2 but not biholomorphic to it. We studied the fake projective plane P2fake = (a = 7, p = 2, ∅, D327) in the Cartwright-Steger classification. In this summer, we exploit the large symmetries given by Aut(P2fake) = C3xC7 to construct a simpler embedding of this surface into CP5 as a system of 56 sextics with coefficients in Q(\sqrt{-7}). For each torsion line bundle T ∈ Pic(P2fake), we also compute and study the linear systems |nH + T| with small n, where H is an ample generator of the Neron-Severi group. Finally, we constructed explicit equations of the fake projective plane $(a = 7, p = 2, ∅, D3X7), a closely related fake projective plane to P2fake.
