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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. The relation is shown to hold for both the Chern– Schwartz–MacPherson class and the Chern–Fulton class. The main tool is a formula for Segre classes of splayed subschemes. We also(More)
We obtain several new characterizations of splayedness for divisors: a Leibniz property for ideals of singularity subschemes, the vanishing of a 'splayed-ness' module, and the requirements that certain natural morphisms of modules and sheaves of logarithmic derivations and logarithmic differentials be isomorphisms. We also consider the effect of splayedness(More)
In this paper we study endomorphism rings of finite global dimension over not necessarily normal commutative rings. These objects have recently attracted attention as noncommutative (crepant) resolutions (NC(C)Rs) of singularities. Our results yield various necessary and sufficient conditions for their existence. We also introduce and study the global(More)
The multiplicity is perhaps the most naive measurement of singularities. Because f is singular at x if all the first order partial derivatives of f vanish there, it is natural to say that f is even more singular if also all the second order partials vanish, and so forth. The order, or multiplicity, of the singularity at x is the largest d such that for all(More)
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