Hostname: page-component-77c89778f8-5wvtr Total loading time: 0 Render date: 2024-07-21T13:51:31.638Z Has data issue: false hasContentIssue false
  • English
  • Français

A Riemann–Hurwitz Theorem for the Algebraic Euler Characteristic

Published online by Cambridge University Press:  20 November 2018

Andrew Fiori
Andrew Fiori*
Affiliation:
Mathematics & Statistics, 612 Campus Place N.W., University of Calgary, 2500 University Drive NW, Calgary, AB, Canada T2N 1N4. e-mail: andrew.fiori@ucalgary.ca
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove an analogue of the Riemann–Hurwitz theorem for computing Euler characteristics of pullbacks of coherent sheaves through finite maps of smooth projective varieties in arbitrary dimensions, subject only to the condition that the irreducible components of the branch and ramification locus have simple normal crossings.

Keywords

14F0514C17Riemann-Hurwitzlogarithmic-Chern classEuler characteristic
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 3 , 01 September 2017 , pp. 490 - 509
Copyright
Copyright © Canadian Mathematical Society 2017

References

[Ful98] Fulton, William, Intersection theory. Second ed., vol. 2. Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag, Berlin, 1998. http://dx.doi.Org/10.1007/978-1-4612-1700-8 Google Scholar
[IzaO3] Izawa, Takeshi, Note on the Riemann-Hurwitz type formula for multiplicative sequences. Proc. Amer. Math. Soc. 131(2003), no. 11, 3583–3588 (electronic). http://dx.doi.Org/10.1090/S0002-9939-03-07118-1 Google Scholar
[Mum77] Mumford, D., Hirzebruch's proportionality theorem in the noncompact case, Invent. Math. 42(1977), 239–272. http://dx.doi.Org/10.1007/BF01389790 Google Scholar
[Stal7] The Stacks Project Authors, Stacks project, http://stacks.math.columbia.edu, 2017.Google Scholar
[Tsu80] Ryuji Tsushima, A formula for the dimension of spaces ofSiegel cusp forms of degree three. Amer. J. Math. 102(1980), no. 5, 937–977. http://dx.doi.Org/!0.2307/2374198 Google Scholar