منابع مشابه
Chern Classes of Blow-ups
We extend the classical formula of Porteous for blowing-up Chern classes to the case of blow-ups of possibly singular varieties along regularly embedded centers. The proof of this generalization is perhaps conceptually simpler than the standard argument for the nonsingular case, involving Riemann-Roch without denominators. The new approach relies on the explicit computation of an ideal, and a m...
متن کاملA Formula for the Chern Classes of Symplectic Blow-ups
It is shown that the formula for the Chern classes (in the Chow ring) of blow-ups of algebraic varieties, due to Porteous and Lascu-Scott, also holds (in the cohomology ring) for blow-ups of symplectic and complex manifolds. This was used by the second-named author in her solution of the geography problem for 8-dimensional symplectic manifolds. The proof equally applies to real blow-ups of arbi...
متن کاملNonpositive curvature of blow - ups
Consider the following situation: MC is a complex manifold of complex dimension n, and DC is a union of smooth complex codimension-one submanifolds (i.e., DC is a smooth divisor). Examples of this situation include: (1) arrangements of projective hyperplanes in CP, as well as various blow-ups of such arrangements along intersections of hyperplanes, (2) nonsingular toric varieties (whereDC is th...
متن کاملIntersection Multiplicity on Blow-ups
A conjecture on vanishing and non-negativity of intersection multiplicity on the blow-up of a regular local ring at its closed point has been proposed. Proofs of vanishing, several special cases of non-negativity and a sufficient condition for non-negativity of this conjecture are described. The topic on intersection multiplicity on vector bundles is also addressed. Introduction. Let X be a reg...
متن کاملOn Blow-Ups and Injectivity of Quivers
This work connects the idea of a “blow-up” of a quiver with that of injectivity, showing that for a class of monic maps Φ, a quiver is Φ-injective if and only if all blow-ups of it are as well. This relationship is then used to characterize all quivers that are injective with respect to the natural embedding of Pn into Cn.
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ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2009
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004109990247