Geometry of algebraic curves

@inproceedings{Arbarello1985GeometryOA,
  title={Geometry of algebraic curves},
  author={Enrico Arbarello and Maurizio Cornalba and Phillip A. Griffiths and J. C. Harris},
  year={1985}
}
Preface.- Guide to the Reader.- Chapter IX. The Hilbert Scheme.- Chapter X. Nodal curves.- Chapter XI. Elementary deformation theory and some applications.- Chapter XII. The moduli space of stable curves.- Chapter XIII. Line bundles on moduli.- Chapter XIV. The projectivity of the moduli space of stable curves.- Chapter XV. The Teichmuller point of view.- Chapter XVI. Smooth Galois covers of moduli spaces.- Chapter XVII. Cycles on the moduli spaces of stable curves.- Chapter XVIII. Cellular… 

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References

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Many details are being swept under the rug here. Also, many pictures were drawn on the board, which do not appear in these notes

  • Many details are being swept under the rug here. Also, many pictures were drawn on the board, which do not appear in these notes

OK, we've seen upper semicontinuity of the ramification sequence

  • OK, we've seen upper semicontinuity of the ramification sequence

So again, let's try to wonder what the " limit " linear series of the V t will be: this should be a bunch of linear series on X, Y

  • So again, let's try to wonder what the " limit " linear series of the V t will be: this should be a bunch of linear series on X, Y

What do we get in the limit? This is what the game of specialization is all about. We let these linear series degenerate at zero, and see what we might get

  • What do we get in the limit? This is what the game of specialization is all about. We let these linear series degenerate at zero, and see what we might get