\begin{equation*}
\DeclareMathOperator\Coim{Coim}
\DeclareMathOperator\Coker{Coker}
\DeclareMathOperator\Ext{Ext}
\DeclareMathOperator\Hom{Hom}
\DeclareMathOperator\Im{Im}
\DeclareMathOperator\Ker{Ker}
\DeclareMathOperator\Mor{Mor}
\DeclareMathOperator\Ob{Ob}
\DeclareMathOperator\Sh{Sh}
\DeclareMathOperator\SheafExt{\mathcal{E}\mathit{xt}}
\DeclareMathOperator\SheafHom{\mathcal{H}\mathit{om}}
\DeclareMathOperator\Spec{Spec}
\newcommand\colim{\mathop{\mathrm{colim}}\nolimits}
\newcommand\lim{\mathop{\mathrm{lim}}\nolimits}
\newcommand\Qcoh{\mathit{Qcoh}}
\newcommand\Sch{\mathit{Sch}}
\newcommand\QCohstack{\mathcal{QC}\!\mathit{oh}}
\newcommand\Cohstack{\mathcal{C}\!\mathit{oh}}
\newcommand\Spacesstack{\mathcal{S}\!\mathit{paces}}
\newcommand\Quotfunctor{\mathrm{Quot}}
\newcommand\Hilbfunctor{\mathrm{Hilb}}
\newcommand\Curvesstack{\mathcal{C}\!\mathit{urves}}
\newcommand\Polarizedstack{\mathcal{P}\!\mathit{olarized}}
\newcommand\Complexesstack{\mathcal{C}\!\mathit{omplexes}}
\newcommand\Pic{\mathop{\mathrm{Pic}}\nolimits}
\newcommand\Picardstack{\mathcal{P}\!\mathit{ic}}
\newcommand\Picardfunctor{\mathrm{Pic}}
\newcommand\Deformationcategory{\mathcal{D}\!\mathit{ef}}
\end{equation*}
50 Algebraic Curves
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Section 50.1: Introduction
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Section 50.2: Curves and function fields
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Section 50.3: Linear series
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Section 50.4: Duality
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Section 50.5: Riemann-Roch
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Section 50.6: Some vanishing results
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Section 50.7: Very ample invertible sheaves
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Section 50.8: The genus of a curve
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Section 50.9: Plane curves
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Section 50.10: Curves of genus zero
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Section 50.11: Geometric genus
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Section 50.12: Riemann-Hurwitz
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Section 50.13: Inseparable maps
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Section 50.14: Pushouts
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Section 50.15: Glueing and squishing
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Section 50.16: Multicross and nodal singularities
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Section 50.17: Torsion in the Picard group
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Section 50.18: Genus versus geometric genus
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Section 50.19: Nodal curves
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Section 50.20: Families of nodal curves
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Section 50.21: More vanishing results
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Section 50.22: Contracting rational tails
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Section 50.23: Contracting rational bridges
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Section 50.24: Contracting to a stable curve
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Section 50.25: Vector fields