On the irreducibility of Severi varieties on 3 surfaces

On the irreducibility of Severi varieties on 3 surfaces

Let ( S , L ) (S,L) be a polarized K 3 K3 surface of genus p ⩾ 11 p \geqslant 11 such that Pic ( S ) = Z [ L ] \textrm {Pic}(S)=\mathbf {Z}[L] and δ \delta is a non-negative integer. We prove that if p ⩾ 4 δ − 3 p\geqslant 4\delta -3 , then the Severi variety of δ \delta -nodal curves in | L | |L| i...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2019-10, Vol.147 (10), p.4233-4244
Hauptverfasser: Ciliberto, C., Dedieu, Th
Format: Artikel
Sprache:eng
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Zusammenfassung:Let ( S , L ) (S,L) be a polarized K 3 K3 surface of genus p ⩾ 11 p \geqslant 11 such that Pic ( S ) = Z [ L ] \textrm {Pic}(S)=\mathbf {Z}[L] and δ \delta is a non-negative integer. We prove that if p ⩾ 4 δ − 3 p\geqslant 4\delta -3 , then the Severi variety of δ \delta -nodal curves in | L | |L| is irreducible.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/14559