Representations of Clifford algebras of ternary quartic forms
Abstract
Given a nondegenerate ternary form f=f(x1,x2,x3) of degree 4 over an algebraically closed field of characteristic zero, we use the geometry of K3 surfaces to construct a certain positive-dimensional family of irreducible representations of the generalized Clifford algebra associated to f. From this we obtain the existence of linear Pfaffian representations of the quartic surface Xf=\w4=f(x1,x2,x3)\, as well as information on the Brill-Noether theory of a general smooth curve in the linear system |OXf(3)|.
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