The first higher Chow groups of ${\mathcal{M}}_{1,n}$ for $n\le 4$

Abstract

For $n\le 4$, we compute the indecomposible higher Chow groups $\overline{\mathrm{CH}}({\mathcal{M}}_{1,n},1)$ with integer coefficients. As an application, we give new proofs of presentations of the integral Chow rings $\mathrm{CH}({\overline{\mathcal{M}}}_{1,n})$ for $n\le 4$ and determine formulas for the classes of boundary strata in these rings.

104 pages. Remarks 2.22 and 2.26 are new, and some typos have been fixed