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Segre’s University Courses and the Blossoming of the Italian School of Algebraic Geometry Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Corrado Segre, Guido Castelnuovo and the Riemann-Roch Theorem

Author : Edoardo Sernesi

Published in: From Classical to Modern Algebraic Geometry

Publisher: Springer International Publishing

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Abstract

We reproduce a self-contained proof of the Riemann-Roch Theorem, originally given by G. Castelnuovo and inspired by ideas of C. Segre.

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previous chapter Geometry of Lines and Degeneracy Loci of Morphisms of Vector Bundles
next chapter Introduction to the Handwritten Notebook on Geometry on Simply Infinite Algebraic Entities (1890–91)
Footnotes
1
This is the key enumerative assumption made by Enriques (1919), which can be fully justified in terms of intersection theory on the symmetric product \( C_{r + 1} \).
 
Literature
Arbarello E., Cornalba M., Griffiths P. and Harris J., Geometry of Algebraic Curves I, Springer Grundlehren b. 267 (1984)
Brill A. and Noether M., Ueber die algebraischen Functionen und ihre Anwendung in der Geometrie. Math. Ann. 7 (1873), 269–310
Castelnuovo G., Ricerche di geometria sulle curve algebriche, Atti R. Accad. Sci. Torino 24 (1889), 196–223
Enriques F., Questioni numerative e loro significato nella geometria sopra le curve algebriche. Rend. Acc. Naz. Lincei (5) 28 (1919), 370–374
Schubert H., Kalkul der Abzahlenden Geometrie, Teubner (Leipzig), 1874
Segre C., Introduzione alla geometria sopra un ente algebrico semplicemente infinito. Annali di Matematica Pura e Applicata (2) 23 (1894), 41–142
Severi F., Trattato di Geometria Algebrica—Volume I Parte I: Geometria delle serie lineari. Zanichelli (Bologna), 1926
Severi F., Prefazione. In Corrado Segre: Opere, vol. I. Cremonese (Roma), 1957
Metadata
Title
Corrado Segre, Guido Castelnuovo and the Riemann-Roch Theorem
Author
Edoardo Sernesi
Copyright Year
2016
Book
From Classical to Modern Algebraic Geometry

Print ISBN: 978-3-319-32992-5

Electronic ISBN: 978-3-319-32994-9

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-32994-9_14

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