Low degree motivic Donaldson-Thomas invariants of the three-dimensional projective space

Research output: Working paper/Preprint › Preprint

Authors

  • Anna M. Viergever

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Original languageEnglish
Number of pages27
Publication statusE-pub ahead of print - 15 Dec 2023

Abstract

Levine has constructed motivic analogues of virtual fundamental classes, living in cohomology of Witt sheaves. We use this to define motivic Donaldson-Thomas invariants \(\tilde{I}_n\) for \(\mathbb{P}^3\) over \(\mathbb{R}\). We show that for \(n\) odd, \(\tilde{I}_n = 0\) and we compute \(\tilde{I}_2 = 10, \tilde{I}_4 = 25\) and \(\tilde{I}_6 = -50\). We then make a conjecture about the general case, which could be a motivic analogue of a classical theorem of Maulik-Nekrasov-Okounkov-Pandharipande. The results presented here also form a chapter in the authors thesis, which was submitted on May 30'th, 2023.

Keywords

    math.AG, 14N35, 14F42

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Low degree motivic Donaldson-Thomas invariants of the three-dimensional projective space. / Viergever, Anna M.
2023.

Research output: Working paper/Preprint › Preprint

Viergever AM. Low degree motivic Donaldson-Thomas invariants of the three-dimensional projective space. 2023 Dec 15. Epub 2023 Dec 15. doi: 10.48550/arXiv.2312.09882
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