Geodesic
Characteristic classes of affine varieties and Plücker formulas for affine morphisms
Journal of the European Mathematical Society, Tome 20 (2018) no. 1, pp. 15-59

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An enumerative problem on a variety V is usually solved by reduction to intersection theory in the cohomology of a compactification of V. However, if the problem is invariant under a “nice” group action on V (so that V is spherical), then many authors suggested a better home for intersection theory: the direct limit of the cohomology rings of all equivariant compactifications of V. We call this limit the affine cohomology of V and construct affine characteristic classes of subvarieties of a complex torus, taking values in the affine cohomology of the torus.
DOI : 10.4171/jems/758
Classification : 14-XX, 32-XX
Keywords: Intersection theory, enumerative geometry, tropical geometry, Newton polytope, discriminant, Thom polynomial, toric variety, spherical variety 
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Alexander Esterov. Characteristic classes of affine varieties and Plücker formulas for affine morphisms. Journal of the European Mathematical Society, Tome 20 (2018) no. 1, pp. 15-59. doi: 10.4171/jems/758

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