Geodesic
Chern Classes of Splayed Intersections
Canadian journal of mathematics, Tome 67 (2015) no. 6, pp. 1201-1218

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DOI

We generalize the Chern class relation for the transversal intersection of two nonsingular varieties to a relation for possibly singular varieties, under a splayedness assumption. We show that the relation for the Chern–Schwartz–MacPherson classes holds for two splayed hypersurfaces in a nonsingular variety, and under a strong splayedness assumption for more general subschemes. Moreover, the relation is shown to hold for the Chern–Fulton classes of any two splayed subschemes. The main tool is a formula for Segre classes of splayed subschemes. We also discuss the Chern class relation under the assumption that one of the varieties is a general very ample divisor.
DOI : 10.4153/CJM-2015-010-7
Mots-clés : 14C17, 14J17, Splayed intersection, Chern-Schwartz-MacPherson class, Chern-Fulton class, splayed blowup, Segre class 
Aluffi, Paolo; Faber, Eleonore. Chern Classes of Splayed Intersections. Canadian journal of mathematics, Tome 67 (2015) no. 6, pp. 1201-1218. doi: 10.4153/CJM-2015-010-7
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     title = {Chern {Classes} of {Splayed} {Intersections}},
     journal = {Canadian journal of mathematics},
     pages = {1201--1218},
     year = {2015},
     volume = {67},
     number = {6},
     doi = {10.4153/CJM-2015-010-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-010-7/}
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