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FIELD Mathematics
DATE May 23 (Thu), 2019
TIME 14:00-15:30
PLACE 1423
SPEAKER Fakhruddin, Najmuddin
HOST Keum, JongHae
INSTITUTE Tata Institute of Fundamental Reseach
TITLE The geometry of 2-adically uniformised fake projective planes II

Fake projective planes are surfaces of general type with the same Betti numbers as the projective planes. The first such surface was constructed by Mumford using p-adic uniformisation with p=2. Subsequently, two other such surfaces were constructed by Ishida and Kato using groups discovered by Cartwright, Mantero, Steger and Zappa. A few years later all such surfaces over the complex numbers were classified by Prasad--Yeung and Cartwright--Steger. In these talks I will explain the construction method of Mumford and then discuss how the explicit geometry of the special fibre of 2-adically uniformised fake projective planes---already used in the case of Mumford's surface by Ishida for other purposes---can be used to study the geometry of these surfaces. In particular, I will discuss how one may compute the cohomology of line bundles on such fake projective planes and applications to exceptional collections and bicanonical maps.

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