Geodesic
A Riemann–Hurwitz Theorem for the Algebraic Euler Characteristic
Canadian mathematical bulletin, Tome 60 (2017) no. 3, pp. 490-509

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DOI

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.
DOI : 10.4153/CMB-2017-022-3
Mots-clés : 14F05, 14C17, Riemann-Hurwitz, logarithmic-Chern class, Euler characteristic 
Fiori, Andrew. A Riemann–Hurwitz Theorem for the Algebraic Euler Characteristic. Canadian mathematical bulletin, Tome 60 (2017) no. 3, pp. 490-509. doi: 10.4153/CMB-2017-022-3
@article{10_4153_CMB_2017_022_3,
     author = {Fiori, Andrew},
     title = {A {Riemann{\textendash}Hurwitz} {Theorem} for the {Algebraic} {Euler} {Characteristic}},
     journal = {Canadian mathematical bulletin},
     pages = {490--509},
     year = {2017},
     volume = {60},
     number = {3},
     doi = {10.4153/CMB-2017-022-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-022-3/}
}
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