Concomitants of Ternary Quartics and Vector-valued Siegel and Teichm\'uller Modular Forms of Genus Three

Autor:	Cléry, Fabien, Faber, Carel, van der Geer, Gerard
Rok vydání:	2019
Předmět:	Mathematics - Algebraic Geometry Mathematics - Number Theory 10D 11F46 14H10 14H45 14J15 14K10
Druh dokumentu:	Working Paper
Popis:	We show how one can use the representation theory of ternary quartics to construct all vector-valued Siegel modular forms and Teichm\"uller modular forms of degree 3. The relation between the order of vanishing of a concomitant on the locus of double conics and the order of vanishing of the corresponding modular form on the hyperelliptic locus plays an important role. We also determine the connection between Teichm\"uller cusp forms on \overline{M}_g and the middle cohomology of symplectic local systems on M_g. In genus 3, we make this explicit in a large number of cases. Comment: 34 pages. In an appendix (joint work of G. Farkas, R. Pandharipande, and the second author) it is shown that Teichm\"uller modular forms extend to \overline{M}_g for g at least 3. Other minor changes
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1908.04248 Zobrazit plný text záznamu View this record from Arxiv