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Abstract des Vortrages von Gavin Brown

Classification of (complex projective) Calabi-Yau 3-folds is still a very long way off, but the ideas of Hirzebruch, Reid, Candelas, Gross and others of the 1980s and 90s, which explain how it may be possible to tie all such families of 3-folds together in a big web, give a place to try to start growing a map of them all. I explain the first examples, the early ideas, and how these apply to construct polarised Calabi-Yau 3-folds with associated homogeneous coordinate rings in codimension 4; the absence of structure results for such rings means we use the Gorenstein unprojection methods of Kustin--Miller and Papadakis--Reid, and this closely mirrors the conifold transitions used to join up the web. This is joint with Konstantin Georgiadis.