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A Characterization of Symplectic Grassmannians

Hold Date 2016-06-09 15:00~2016-06-09 16:30

Place Seminar Room W1-D-610, West Zone 1, Ito campus, Kyushu University

Object person  

Speaker Kiwamu WATANABE (Saitama University)

In the series of their works, J. M. Hwang and N. Mok have been developing the theory of Varieties of Minimal Rational Tangents (VMRT for short). In this direction, the results of Mok and J. Hong-Hwang allow us to recognize a homogeneous Fano manifold X of Picard number one by looking at its VMRT at a general point. This characterization works for all rational homogeneous manifolds of Picard number one whenever the VMRT is rational homogeneous, which is always the case except for the short root cases; namely for symplectic Grassmannians, and for two varieties of type F4.

In this talk we show that, if we impose that the VMRT is the expected one at every point of the variety, we may still characterize symplectic Grassmannians.
This is a joint work with G. Occhetta and L. E. Sola Conde