 The Riemann-Roch TheoremAudun Holme ()
Chapter Chapter 20 in A Royal Road to Algebraic Geometry, 2012, pp 329-334 from Springer Abstract: Abstract This chapter is on the Riemann-Roch Theorem. We start with Hirzebruch’s Riemann-Roch Theorem, and deduce from it the Riemann-Roch Theorem for curves, and for surfaces. We state the general Grothendieck’s Riemann-Roch theorem, deducing that of Hirzebruch from it. Some general constructions and concepts used in this chapter have been extended so that schemes with singularities are covered. This theory is developed in the paper (Publ. Math. l’HIES, 45:147–167, 1975) and in the book (Intersection Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, 1st edn., vol. 2. Springer, Berlin, 1984 and 2nd edn. 1998) by W. Fulton. One of the most important applications of this marvelous work is the general Baum-Fulton-McPehrson Riemann-Roch Theorem for singular varieties (in Baum et al., Publ. Math. l’HIES, 45, 101–145, 1975). However, we do not include a survey of this work here, as it reaches beyond the scope of the present book. The non singular case is challenging enough at this stage, but the theorem proved in Baum et al. (Publ. Math. l’HIES, 45, 101–145, 1975) would be an exiting source for further study! Keywords: Riemann-Roch Theorem; General Grothendieck; Hirzebruch; Marvelous Work; Singular Varieties (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-19225-8_20 Ordering information: This item can be ordered from DOI: 10.1007/978-3-642-19225-8_20 Access Statistics for this chapter More chapters in Springer Books from Springer |
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