On motivic and arithmetic refinements of Donaldson-Thomas invariants

• Verfasst von: Espreafico, Felipe [VerfasserIn]
• Verfasst von: Walcher, Johannes [VerfasserIn]
• Titel: On motivic and arithmetic refinements of Donaldson-Thomas invariants
• Verf.angabe: Felipe Espreafico and Johannes Walcher
• Ausgabe: Version V2
• E-Jahr: 2023
• Jahr: 27 Jul 2023
• Umfang: 16 S.
• Fussnoten: Gesehen am 16.09.2024
• Titel Quelle: Enthalten in: Arxiv
• Ort Quelle: Ithaca, NY : Cornell University, 1991
• Jahr Quelle: 2023
• Band/Heft Quelle: (2023) vom: Juli, Artikel-ID 2307.03655, Seite 1-16
• DOI: doi:10.48550/arXiv.2307.03655
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 14N35, 81T30
• Sach-SW: High Energy Physics - Theory
• Sach-SW: Mathematics - Algebraic Geometry
• K10plus-PPN: 190257379X

Abstract

In recent years, a version of enumerative geometry over arbitrary fields has been developed and studied by Kass-Wickelgren, Levine, and others, in which the counts obtained are not integers but quadratic forms. Aiming to understand the relation to other "refined invariants", and especially their possible interpretation in quantum theory, we explain how to obtain a quadratic version of Donaldson-Thomas invariants from the motivic invariants defined in the work of Kontsevich and Soibelman and pose some questions. We calculate these invariants in a few simple examples that provide standard tests for these questions, including degree zero invariants of $\mathbb A^3$ and higher-genus Gopakumar-Vafa invariants recently studied by Liu and Ruan. The comparison with known real and complex counts plays a central role throughout.