On the Hitchin fibration for algebraic surfaces
Speaker: Ngo Bao Chau

Time: 9h00, Wednesday, December 13, 2017
Room semina, Floor 6th, Building A6,, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi

Abstract: We explore the structure of the Hitchin fibration for higher dimensional algebraic varieties with emphasis in the case of surfaces. In his original paper, which addresses the case of curves, Hitchin constructs certain spectral curves whose compactified Jacobians can be identified with the fibers in the Hitchin fibration. In higher dimension case, one can construct canonical spectral covers with possibly “very bad” singularities. In the surface cases, we can construct canonical finite Cohen-Macaulayfications of spectral covers. These Cohen-Macaulayfication spectral covers are instrumental in describing Hitchin fibers. It would be very interesting to find Cohen-Macaulayfication of spectral covers in dimension >2


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