Self-dual Metrics and Twenty-eight Bitangents
نویسنده
چکیده
We prove that there is a one-to-one correspondence between selfdual metrics on 3CP of positive scalar curvature admitting a non-trivial Killing field but not being conformal to LeBrun metrics, and a class of normal quartic surfaces in CP whose equations can be explicitly written down. As a consequence, we show that the moduli space of these self-dual metrics on 3CP is non-empty and diffeomorphic to R. In our proof, a key role is played by a classical result in algebraic geometry that a smooth plane quartic always possesses twenty-eight bitangents.
منابع مشابه
Almost - Kähler Anti - Self - Dual Metrics
of the Dissertation Almost-Kähler Anti-Self-Dual Metrics by Inyoung Kim Doctor of Philosophy in Mathematics Stony Brook University 2014 We show the existence of strictly almost-Kähler anti-self-dual metrics on certain 4-manifolds by deforming a scalar-flat Kähler metric. On the other hand, we prove the non-existence of such metrics on certain other 4-manifolds by means of SeibergWitten theory. ...
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