21 dec 2016 -- 15:00
Aula di Consiglio, Dip.Matematica, Università "La Sapienza", Roma
Abstract.
Let Σ be a Riemann surface and M a compact, simply connected hyper-Kähler manifold of real dimension 4, and let X be an isometric immersion of Σ in M.
From a covariantly constant spinor one can costruct a complex structure on M that makes it a K3 surface. Then, what I prove is that X is a holomorphic map with respect to such structure on M if and only if the spinor is annihilated by some projector associated to X. From this fact we recover the identification, well-known in super-symmetric string theory, of BPS states on a K3 with holomorphic vertical curves on its twistor family.