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  "body": "\n## Summary\n\nThe Todd class is a characteristic class of vector bundles, built from the [[Chern classes|PAD37GKDPD]] by a fixed power series.\nThe Todd class of a smooth variety is the Todd class of its tangent bundle.\nIt is the correction term in the [[Hirzebruch–Riemann–Roch theorem|G3X02FKQCR]] and the [[Grothendieck–Riemann–Roch theorem|3HKREN3Y3F]], which compute Euler characteristics of sheaves from Chern classes.\n\n## Explanations\n\n### L1 human\n\nThe Riemann–Roch theorem expresses the dimension of a space of sections, an analytic quantity, through numbers such as degrees and the genus.\nIn higher dimensions the right expression needs a universal polynomial in the Chern classes of the tangent bundle, and this polynomial is the Todd class.\nFor a curve of genus $g$, the Todd class is $1 + \\frac{1}{2} c_1$, and its degree part gives the term $1 - g$ in the Riemann–Roch formula $\\chi(L) = \\deg L + 1 - g$.\n",
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