Counting Divisors with Prescribed Singularities

DOI10.2307/1998661zbMath0475.14047OpenAlexW4255437421MaRDI QIDQ3931554

Israel Vainsencher

Publication date: 1981

Full work available at URL: https://doi.org/10.2307/1998661

zbMATH Keywords

contact conditionsmultiplicitiesnumber of divisorsmultiple pointsfamilies of divisorsscheme of zeroes

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Singularities of surfaces or higher-dimensional varieties (14J17) Enumerative problems (combinatorial problems) in algebraic geometry (14N10) Divisors, linear systems, invertible sheaves (14C20) Singularities of curves, local rings (14H20)

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Enumeration of curves with one singular point ⋮ The complement of a generic hypersurface of degree 2n in \(CP^ n\) is not hyperbolic ⋮ The Convex Hull of a Variety ⋮ PGL2-equivariant strata of point configurations in P1 ⋮ Enumeration of cones with singular base ⋮ Rational cuspidal curves on del-Pezzo surfaces ⋮ Enumeration of singular algebraic curves ⋮ On the variety of plane curves of degree \(d\) with a singular point of multiplicity \(m\) ⋮ The enumeration of simultaneous higher-order contacts between plane curves ⋮ Weierstrass points and their impact in the study of algebraic curves: a historical account from the ``Lückensatz to the 1970s ⋮ Limits of Pluri–Tangent Planes to Quartic Surfaces ⋮ Complex and tropical counts via positive characteristic ⋮ Degree of strata of singular cubic surfaces

Cites Work

• Rational equivalence on singular varieties
• Sistemi lineari di divisori sulle curve e sulle superficie
• Symmetric products of an algebraic curve
• La théorie des classes de Chern
• Secant Bundles on Symmetric Products
• LECTURES ON THEK-FUNCTOR IN ALGEBRAIC GEOMETRY
• Numerical Invariants and Multiple Planes
• The Secant Bundle of a Projective Variety
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