Affine $E_8$ basic representation bundles over rational surfaces with $c^2_1= 0$

Rational surfaces with $c^2_1= 0$ are $\mathbb{P}^2$ blown up at $n = 9$ points (or $\mathbb{F}_m$ blown up at $8$ points). When $n \leq 8$, lines on such surfaces ($\mathbb{P}^2$ blown up at $n$ points) give rise to $E_n$ representation bundles over them. When $n = 9$, there exists infinitely many lines. We use them to construct an affine $E_8$ basic representation bundle. Its VOA structure is determined by line configuration of such surfaces.

Keywords

rational surface, basic representation, bundle

2010 Mathematics Subject Classification

14H60, 14J26

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Published 25 March 2015