Multiple-point formulas. I: Iteration

DOI10.1007/BF02392866zbMath0479.14004WikidataQ94817658 ScholiaQ94817658MaRDI QIDQ1161567

Steven Lawrence Kleiman

Publication date: 1981

Published in: Acta Mathematica (Search for Journal in Brave)

zbMATH Keywords

enumerative geometrymultiple-point formulassingularities of mappingspositive cycledouble-point formular-fold pointsresidual-intersection theorytriple-point formula

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Global theory and resolution of singularities (algebro-geometric aspects) (14E15) Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry (14C17) Enumerative problems (combinatorial problems) in algebraic geometry (14N10)

Related Items (39)

Space curves on surfaces with ordinary singularities ⋮ Singularities of Mappings ⋮ Characteristic Classes ⋮ On the coexistence of corank 1 multisingularities of a stable smooth mapping of equidimensional manifolds ⋮ Threefolds in ℙ⁵with One Apparent Quadruple Point ⋮ Betti numbers of curves and multiple-point loci ⋮ Genus of the intersection curve of two rational surface patches ⋮ Enumerating stationary multiple-points ⋮ Structure of node polynomials for curves on surfaces ⋮ Surfaces in \(\mathbb{P}^4\) whose 4-secant lines do not sweep out a hypersurface ⋮ Singularities of mappings on ICIS and applications to Whitney equisingularity ⋮ Le Potier's strange duality, quot schemes, and multiple point formulas for del Pezzo surfaces ⋮ Strongly Cohen-Macaulay Schemes and Residual Intersections ⋮ Iterated multiple points I: Equations and pathologies ⋮ Moment maps and cohomology of non-reductive quotients ⋮ Reflection maps ⋮ On submaximal plane curves. ⋮ Enriques diagrams, arbitrarily near points, and Hilbert schemes ⋮ Coincidence formulas for line complexes ⋮ Conditions imposed by tacnodes and cusps ⋮ A united-set formula ⋮ Eight-secant conics for space curves ⋮ On the existence of plane curves with imposed multiple points ⋮ Stationary Points of Plane Forms ⋮ Contribution des droites d'une surface à ses multisécantes ⋮ The topology of corank 1 multi-singularities of stable smooth mappings of equidimensional manifolds ⋮ The enumeration of simultaneous higher-order contacts between plane curves ⋮ Unnamed Item ⋮ Curves having one place at infinity and linear systems on rational surfaces ⋮ Intersection Theory of Linear Embeddings ⋮ La variété des triplets complets. (The variety of complete triplets) ⋮ Lower semi-continuity of the Waldschmidt constants ⋮ The multiple-point schemes of a finite curvilinear map of codimension one ⋮ Compactifications des espaces de configuration dans les schémas de Hilbert ⋮ Unnamed Item ⋮ Surfaces in \(\mathbb{P}^5\) which do not admit trisecants ⋮ Curvilinear enumerative geometry ⋮ Degree of strata of singular cubic surfaces ⋮ On the universal scheme of r-relative clusters of a family

Cites Work

• Compactifying the Picard scheme
• On the symmetric and Rees algebra of an ideal generated by a d-sequence
• On multiple points of smooth immersions
• A geometric approach to the arithmetic genus of a projective manifold of dimension three
• Immersion and embedding of projective varieties
• A note on residual intersections and the double point formula
• Residual intersections and Todd's formula for the double locus of a morphism
• Secant Bundles and Todd's Formula for the Double Points of Maps into P ⁿ
• The Cotangent Complex of a Morphism
• Residual intersections in Cohen-Macaulay rings
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