Abstract
Given a general 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 and van den Bergh’s correspondence between representations of the generalized Clifford algebra Cf associated to f and Ulrich bundles on the surface Xf := {w = f(x1, x2, x3)} ⊆ P to construct a positive-dimensional family of 8-dimensional irreducible representations of Cf . The main part of our construction, which is of independent interest, uses recent work of Aprodu-Farkas on Green’s Conjecture together with a result of Basili on complete intersection curves in P to produce simple Ulrich bundles of rank 2 on a smooth quartic surface X ⊆ P with determinant OX(3). This implies that every smooth quartic surface in P is the zerolocus of a linear Pfaffian, strengthening a result of Beauville-Schreyer on general quartic surfaces. 2010 Mathematics Subject Classification: 14J60 (13C14, 16G30)
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