Representations of Clifford algebras of ternary quartic forms

Emre Coskun; Rajesh S. Kulkarni; Yusuf Mustopa

Representations of Clifford algebras of ternary quartic forms

Algebraic Geometry 2011-03-08 v3 Rings and Algebras

Authors: Emre Coskun , Rajesh S. Kulkarni , Yusuf Mustopa

Abstract

Given a nondegenerate ternary form $f=f(x_1,x_2,x_3)$ 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 $X_f=\{w^4=f(x_1,x_2,x_3)\},$ as well as information on the Brill-Noether theory of a general smooth curve in the linear system $|\mathcal{O}_{X_f}(3)|.$

Keywords

Clifford algebras ternary quartic forms K3 surfaces Pfaffian representations Brill-Noether theory quartic surfaces

Cite

@article{arxiv.1103.0529,
  title  = {Representations of Clifford algebras of ternary quartic forms},
  author = {Emre Coskun and Rajesh S. Kulkarni and Yusuf Mustopa},
  journal= {arXiv preprint arXiv:1103.0529},
  year   = {2011}
}

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Representations of Clifford algebras of ternary quartic forms

Abstract

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