| 研究実績の概要 |
Under the support of my JSPS KAKENHI Grant Number JP19K23397, I have been making progress towards the research aims of the planned proposal. With my collaborators, we use localization formulae to compute Donaldson-Thomas invariants of Calabi-Yau 4-folds in several different settings. The output is that I wrote three research papers (with my collaborators) since September of 2019. To be specific, I wrote a paper "Curve counting via stable objects in derived categories of Calabi-Yau 4-folds" with Yukinobu Toda, where we defined the category of D0-D2-D8 bounded states and used it to give a wall-crossing explanation of the Gopakumar-Vafa type formula for stable pair invariants of Calabi-Yau 4-folds proposed by Maulik-Toda and myself. I wrote another paper with Yukinobu Toda, named "Gopakumar-Vafa type invariants on Calabi-Yau 4-folds via descendent insertions", where we gave a sheaf theoretic interpretation of Gopakumar-Vafa type invariants of Calabi-Yau 4-folds defined by Klemm-Pandharipande using Donaldson-Thomas invariants of one dimensional stable sheaves with descendent insertions. The third paper "Stable pair invariants of local Calabi-Yau 4-folds" is with Martijn Kool and Sergej Monavari from Utrecht University, the Netherlands, where we computed stable pair invariants by several methods, including using localization formulae to verify a conjecture of Maulik-Toda and myself.
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