Hodge Representations. (17th November 2020)

• Record Type: Journal Article
• Authors: Clingher, Adrian; Han, Xiayimei; Robles, Colleen
• Is Part Of: Experimental results. Volume 1(2020)
• Publication Date: 2020-11-17
• Subjects: 58A14; Hodge theory; Science -- Experiments -- Periodicals; Science -- Methodology -- Periodicals; 507.24
• DOI: 10.1017/exp.2020.55
• Languages: English
• ISSNs: 2516-712X

Abstract

Abstract: Green–Griffiths–Kerr introduced Hodge representations to classify the Hodge groups of polarized Hodge structures, and the corresponding Mumford–Tate subdomains. We summarize how, given a fixed period domain $ \mathcal{D} $, to enumerate the Hodge representations and corresponding Mumford–Tate subdomains $ D \subset \mathcal{D} $ . The procedure is illustrated in two examples: (i) weight two Hodge structures with $ {p}_g={h}^{2, 0}=2 $ ; and (ii) weight three CY-type Hodge structures.