Configuration of lines in del Pezzo surfaces with Gosset Polytopes

Lee, Jae-Hyouk

doi:10.48550/arxiv.1001.4174

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2013

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“…If we restrict it to the anti-canonical curve in X, which is an elliptic curve Σ, then we obtain an isomorphism between the moduli space of degree 9 − n del Pezzo surfaces which contain Σ and the moduli space of E n -bundles over Σ. This work is motivated from string/F -theory duality, and it has been studied extensively by Friedman-Morgan-Witten [8] [9][10], Donagi [3][4] [5][7], Leung-Zhang [14][15] [16] and others [6] [13] [17] [18].…”

Section: Introductionmentioning

confidence: 99%

ADE Bundles over Surfaces with ADE Singularities

Chen¹,

Leung²

2013

International Mathematics Research Notices

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Given a compact complex surface X with an ADE singularity and pg = 0, we construct ADE bundles over X and its minimal resolution Y . Furthermore, we descibe their minuscule representation bundles in terms of configurations of (reducible) (−1)-curves in Y .1 Here V is the lowest weight representation with lowest weight dual to −C k , i.e. V is dual to the highest weight representation with highest weight dual to C k .2 Unless specify otherwise, C i always refers to an irreducible component of C, i.e. i = 0.

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