Intersection multiplicity of Serre on regular schemes

Intersection 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...

Multiplicity of a Noetherian Intersection

A differential ring of analytic functions in several complex variables is called a ring of Noetherian functions if it is finitely generated as a ring and contains the ring of all polynomials. In this paper, we give an effective bound on the multiplicity of an isolated solution of a system of n equations fi = 0 where fi belong to a ring of Noetherian functions in n complex variables. In the one-...

Multiplicity of Jet Schemes of Monomial Schemes

This article studies jet schemes of monomial schemes. They are known to be equidimensional but usually are not reduced [13]. We thus investigate their structure further, giving a formula for the multiplicity along every component of the jet schemes of a general reduced monomial hypersurface (that is, the case of a simple normal crossing divisor).

Intersection Theory on Regular Schemes via Alterations and Deformation to the Normal Cone Dissertation

Reconstructing Projective Schemes from Serre Subcategories

Given a positively graded commutative coherent ring A = ⊕j>0Aj , finitely generated as an A0-algebra, a bijection between the tensor Serre subcategories of qgrA and the set of all subsets Y ⊆ Proj A of the form Y =