The Severi problem for Hirzebruch surfaces
Vsevolod Shevchishin
TL;DR
This paper proves that the set of irreducible nodal curves with fixed class and genus on a Hirzebruch surface is irreducible, advancing understanding of algebraic curve moduli on these surfaces.
Contribution
It establishes the irreducibility of the locus of irreducible nodal curves on Hirzebruch surfaces for given class and genus, a significant result in algebraic geometry.
Findings
Locus of irreducible nodal curves is irreducible on Hirzebruch surfaces.
Supports the structure theory of algebraic curves on complex surfaces.
Provides tools for studying moduli spaces of curves.
Abstract
We prove that the locus of irreducible nodal curves on a given Hirzebruch surface F_k of given linear equivalency class and genus g is irreducible.
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Taxonomy
TopicsMathematics and Applications · Algebraic Geometry and Number Theory · Geometric and Algebraic Topology