Geometry of families of nodal curves on the blown-up projective plane

DOI10.1090/S0002-9947-98-02055-8zbMath0889.14010arXivalg-geom/9601020OpenAlexW1838085926MaRDI QIDQ4382925

Gert-Martin Greuel, Christoph Lossen, Eugenii I. Shustin

Publication date: 24 March 1998

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/alg-geom/9601020

zbMATH Keywords

irreducible curveblown-up projective planeexistence of nodal curvesfamilies of reducible curves

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Singularities of curves, local rings (14H20)

Related Items

New asymptotics for the existence of plane curves with prescribed singularities, Logarithmic asymptotics of the genus zero {G}romov-{W}itten invariants of the blown up plane, Welschinger invariants of real del Pezzo surfaces of degree ≥ 2, Severi varieties on blow‐ups of the symmetric square of an elliptic curve, Curves and symmetric spaces. II., Nonemptiness of severi varieties on enriques surfaces, Minitwistor spaces, Severi varieties, and Einstein-Weyl structure, Welschinger invariants of real Del Pezzo surfaces of degree \(\geq 3\), The existence of plane curves with prescribed singularities, SOME RESULTS OF REGULARITY FOR SEVERI VARIETIES OF PROJECTIVE SURFACES, Smoothness of equisingular families of curves, Braid monodromy of algebraic curves, Intersection of plane curves and construction of curves with ordinary singularities, Existence of curves with prescribed topological singularities, Irreducibility of equisingular families of curves, Families of nodal curves on projective threefolds and their regularity via postulation of nodes, The moduli of singular curves on \(K3\) surfaces, On the irreducibility of the Severi variety of nodal curves in a smooth surface, Plane Algebraic Curves with Prescribed Singularities

Cites Work

• Families of curves on surfaces
• Families of plane curves and their limits: Enriques' conjecture and beyond
• On the Severi problem
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• Footnotes to a paper of Beniamino Segre. (The number of \(g^1_d\)'s on a general \(d\)-gonal curve, and the unirationality of the Hurwitz spaces of 4-gonal and 5-gonal curves)
• Families of curves with nodes on K-3 surfaces
• Real plane algebraic curves with prescribed singularities
• Equianalytic and equisingular families of curves on surfaces
• Une conjecture pour la cohomologie des diviseurs sur les surfaces rationelles génériques.
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