TY - UNPB

T1 - Low degree motivic Donaldson-Thomas invariants of the three-dimensional projective space

AU - Viergever, Anna M.

N1 - 27 pages, citations added to the introduction

PY - 2023/12/15

Y1 - 2023/12/15

N2 - 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.

AB - 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.

KW - math.AG

KW - 14N35, 14F42

U2 - 10.48550/arXiv.2312.09882

DO - 10.48550/arXiv.2312.09882

M3 - Preprint

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

ER -