David Eisenbud, University of California, Berkeley, CA, and Joe Harris, Harvard University, Cambridge, MA

• IntroductionLinear series and morphisms to projective spaceThe Riemann-Roch theoremCurves of genus 0Smooth plane curves and curves of genus 1JacobiansHyperelliptic curves and curves of genus 2 and 3Fine moduli spacesModuli of curvesCurves of genus 4 and 5Hyperplane sections of a curveMonodromy of hyperplane sectionsBrill-Noether theory and applications to genus 6Inflection pointsProof of the Brill-Noether theoremUsing a singular plane modelLinkage and the canonical sheave of a singular curvesScrolls and the curves they containFree resolutions and canonical curvesHilbert schemesAppendix A: A historical essay on some topics in algebraic geometry (by Jeremy Gray)Hints to marked exercisesBibliographyIndex

David Eisenbud, University of California, Berkeley, CA, and Joe Harris, Harvard University, Cambridge, MA

• IntroductionLinear series and morphisms to projective spaceThe Riemann-Roch theoremCurves of genus 0Smooth plane curves and curves of genus 1JacobiansHyperelliptic curves and curves of genus 2 and 3Fine moduli spacesModuli of curvesCurves of genus 4 and 5Hyperplane sections of a curveMonodromy of hyperplane sectionsBrill-Noether theory and applications to genus 6Inflection pointsProof of the Brill-Noether theoremUsing a singular plane modelLinkage and the canonical sheave of a singular curvesScrolls and the curves they containFree resolutions and canonical curvesHilbert schemesAppendix A: A historical essay on some topics in algebraic geometry (by Jeremy Gray)Hints to marked exercisesBibliographyIndex

David Eisenbud, University of California, Berkeley, CA, and Joe Harris, Harvard University, Cambridge, MA

• IntroductionLinear series and morphisms to projective spaceThe Riemann-Roch theoremCurves of genus 0Smooth plane curves and curves of genus 1JacobiansHyperelliptic curves and curves of genus 2 and 3Fine moduli spacesModuli of curvesCurves of genus 4 and 5Hyperplane sections of a curveMonodromy of hyperplane sectionsBrill-Noether theory and applications to genus 6Inflection pointsProof of the Brill-Noether theoremUsing a singular plane modelLinkage and the canonical sheave of a singular curvesScrolls and the curves they containFree resolutions and canonical curvesHilbert schemesAppendix A: A historical essay on some topics in algebraic geometry (by Jeremy Gray)Hints to marked exercisesBibliographyIndex