For [*bipartite conical*]{} curves the calculation of the Brauer group can be carried out using only the Brauer groups of fields.

\[c4\] Let $C=C^+\cup C^-$ be a bipartite conical curve, and let $\Lambda=\Lambda^+\coprod\Lambda^-$ be the corresponding decomposition of $\Lambda$. Then $\operatorname{Br}(C)$ is the kernel of the map $$\bigoplus_{\lambda\in\Lambda^+}\operatorname{Br}(k(\lambda))/[\wtl C_\lambda]\ \oplus\
\bigoplus_{\lambda\in\Lambda^-}\operatorname{Br}(k(\lambda))/[\wtl C_\lambda]\
\lrar \operatorname{Br}(C^+\cap C^-),$$ where $[\wtl C_\lambda]\in \operatorname{Br}(k(\lambda))$ is the class of the conic $\wtl C_\lambda$ over the field $k(\lambda)$, and the map $\operatorname{Br}(k(\lambda))/[\wtl C_\lambda]\to \operatorname{Br}(C^+\cap C^-)$ is the restriction followed by multiplication by $\pm 1$ when $\lambda\in\Lambda^\pm$.

This follows directly from Proposition \[p3\] and the well known fact that the Brauer group of a conic over $k$ is the quotient of $\operatorname{Br}(k)$ by the cyclic subgroup generated by the class of this conic.

In some cases one can compute $\operatorname{Br}(C)$ using the Hochschild–Serre spectral sequence $H^p(k,H^q(\ovl C,{\mathbb{G}}_m))\Rightarrow H^{p+q}(C,{\mathbb{G}}_m)$. In [@GB III, Cor. 1.2] Grothendieck proved that $\operatorname{Br}(\ovl{C}) = 0$ for any curve $C$. Hence the spectral sequence identifies the cokernel of the natural map $\operatorname{Br}(k)\to \operatorname{Br}(C)$ with a subgroup of $H^1(k,\operatorname{Pic}(\ovl C))$.

The structure of $\Gamma_k$-module $\operatorname{Pic}(\ovl C)$ is well known, at least up to its maximal unipotent subgroup. It is convenient to describe this structure in combinatorial 