Titlebook: Categorical Donaldson-Thomas Theory for Local Surfaces; Yukinobu Toda Book 2024 The Editor(s) (if applicable) and The Author(s), under exc

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Categorified Hall Products on DT Categories,In this chapter, we use categorified Hall products for DT categories to give an approach toward Conjectures . and ..

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Some Auxiliary Results,In this chapter, we prove several technical results which were postponed in previous sections.

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https://doi.org/10.1007/978-3-031-61705-8Donaldson-Thomas theory; Calabi-Yau 3-Folds; Derived Categories; Matrix Factorizations; Derived Algebrai

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978-3-031-61704-1The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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Introduction,ated to several branches of mathematics, e.g. enumerative geometry, geometric representation theory, birational geometry, classical moduli theory, and so on. Among them, we focus on motivations from d-critical D/K equivalence conjecture and categorical wall-crossing formula.

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Categorical Wall-Crossing via Koszul Duality,omplement of the fully-faithful functor, which recovers the wall-crossing formula of the PT invariants, and also gives a rationality statement of the generating series of PT categories in the Grothendieck group of triangulated categories.

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0075-8434 eraction of enumerative geometry with several other subjects.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

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Book 2024try, 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 equivalenc