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A Riemann-Hurwitz Theorem for the Algebraic Euler Characteristic

  Published:2017-06-07
 Printed: Sep 2017
  • Andrew Fiori,
    Mathematics & Statistics, 612 Campus Place N.W., University of Calgary, 2500 University Drive NW, Calgary, AB, Canada T2N 1N4
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Abstract

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: Riemann-Hurwitz, logarithmic-Chern class, Euler characteristic Riemann-Hurwitz, logarithmic-Chern class, Euler characteristic
MSC Classifications: 14F05, 14C17 show english descriptions Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
Intersection theory, characteristic classes, intersection multiplicities [See also 13H15]
14F05 - Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
14C17 - Intersection theory, characteristic classes, intersection multiplicities [See also 13H15]
 

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