K3 surfaces of type D: moduli and automorphisms

Location: 11th Floor Lecture Hall Speaker Shigeru Mukai, Kyoto University Session Chair Eyal Markman, University of Massachusetts Amherst Abstract An algebraic K3 surface is of type D if the Picard lattice is isometric to the sublattice of even elements in an odd unimodular lattice. Such a K3 surface with Picard number n exists up to n = 20 over the complex number field and is parametrized by an open subset of a locally symmetric space of dimension 20 - n. We describe its moduli and automorphism group explicitly using results of Vinberg on fundamental domains (and on Leech roots of Conway-Sloane). If time permits, we discuss a higher dimensional hyperkahler analogue of K3^[3]-type etc. and/or exceptional phenomena in characteristic p = 2.