On Severi varieties on Hirzebruch surfaces
نویسنده
چکیده
In the current paper we prove that any Severi variety on a Hirzebruch surface contains a unique component parameterizing irreducible nodal curves of the given genus in characteristic zero.
منابع مشابه
On Severi varieties and Moduli spaces of curves in arbitrary characteristic
In the current paper we prove the irreducibility of Severi varieties on Hirzebruch surfaces in arbitrary characteristic. Our approach is of purely algebro-geometric nature, and it works in any characteristic. As a result, we obtain a deformation-theoretic proof of the irreducibility of moduli spaces Mg in positive characteristic, which does not involve reduction to characteristic zero.
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