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# Asian Journal of Mathematics

## Volume 19 (2015)

### Number 2

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

Pages: 307 – 320

DOI: http://dx.doi.org/10.4310/AJM.2015.v19.n2.a6

#### Author

#### Abstract

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