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For a connected boundary $\\partial Y$ of genus $g$, the index is given by $\\int_{\\partial Y}c_1(\\nu_X)+1-g$, where $\\nu_X$ denotes the orthogonal complement of $T\\partial Y$ in $TX_{|\\partial Y}$ and $c_1(\\nu_X)$ the first Chern class of $\\nu_X$ with respect to its natural complex structure. 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