Liou, Jia-Ming (Frank); Schwarz, Albert Weierstrass cycles in moduli spaces and the Krichever map. (English) Zbl 1393.14022 Math. Res. Lett. 24, No. 6, 1739-1758 (2017). Let \(\widehat{\mathcal C \mathcal M}_g\) be the moduli space of triples \((C,p,z)\) where \(C\) is a projective integral curve of genus \(g\), \(p\) is a nonsingular point, and \(z\) is a local coordinate system at \(p\) sending a closed set \(D\) containing \(p\) onto the unit disk with \(z(p) = 0\). Let \(k: \widehat{\mathcal C \mathcal M}_g \to \mathrm{Gr}(\mathcal H)\) be the extended Krichever map that embeds \(\widehat{\mathcal C \mathcal M}_g\) into the Sato Grassmannian \(\mathrm{Gr}(\mathcal H)\) in the sense of G. Segal and G. Wilson [in: Surveys in differential geometry. Vol. IV: Integral systems [Integrable systems]. Lectures on geometry and topology. Cambridge, MA: International Press. 403–466 (1998; Zbl 0939.35163)]. The authors study the \(S^1\)-equivariant cohomology induced by the Krichever map \(k\) and express the answers in terms of tautological classes \(\lambda\) and \(\psi\), where \(\lambda\) are the Chern classes of the Hodge bundle and \(\psi\) is the cotangent line class associated to the marked point \(p\). As applications, the authors compute the Weierstrass cycle class when it has expected dimension and obtains some relations for the tautological ring of the moduli space of curves. Reviewer: Dawei Chen (Chestnut Hill) Cited in 2 Documents MSC: 14H10 Families, moduli of curves (algebraic) Keywords:Krichever map; Weierstrass cycle; moduli space of curves; tautological ring Citations:Zbl 0939.35163 PDFBibTeX XMLCite \textit{J.-M. Liou} and \textit{A. Schwarz}, Math. Res. Lett. 24, No. 6, 1739--1758 (2017; Zbl 1393.14022) Full Text: DOI arXiv