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Categorical Donaldson-Thomas Theory for Local Surfaces

Posted By: hill0
Date: 7 Jul 2024 16:57:05
Categorical Donaldson-Thomas Theory for Local Surfaces

Categorical Donaldson-Thomas Theory for Local Surfaces
English | 2024 | ISBN: 3031617045 | 323 Pages | PDF EPUB (True) | 30 MB

This book provides an introduction to categorical Donaldson-Thomas (DT) theory, a rapidly developing field which has close links to enumerative geometry, birational geometry, geometric representation theory and classical moduli problems in algebraic geometry. The focus is on local surfaces, i.e. the total spaces of canonical line bundles on algebraic surfaces, which form an interesting class of Calabi-Yau 3-folds. Using Koszul duality equivalences and singular support theory, dg-categories are constructed which categorify Donaldson-Thomas invariants on local surfaces. The DT invariants virtually count stable coherent sheaves on Calabi-Yau 3-folds, and play an important role in modern enumerative geometry, representation theory and mathematical physics.
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