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On the irreducibility of Severi varieties on $K3$ surfaces

Authors: C. Ciliberto and Th. Dedieu
Journal: Proc. Amer. Math. Soc. 147 (2019), 4233-4244
MSC (2010): Primary 14H15, 14J28
Published electronically: July 8, 2019
MathSciNet review: 4002538
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Abstract: Let $(S,L)$ be a polarized $K3$ surface of genus $p \geqslant 11$ such that $\textrm {Pic}(S)=\mathbf {Z}[L]$ and $\delta$ is a non-negative integer. We prove that if $p\geqslant 4\delta -3$, then the Severi variety of $\delta$-nodal curves in $|L|$ is irreducible.

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Additional Information

C. Ciliberto
Affiliation: Dipartimento di Matematica, Università degli Studi di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma, Italy
MR Author ID: 49480

Th. Dedieu
Affiliation: Institut de Mathématiques de Toulouse, UMR5219, Université de Toulouse, CNRS, UPS IMT, F-31062 Toulouse Cedex 9, France
MR Author ID: 890662

Received by editor(s): October 15, 2018
Received by editor(s) in revised form: January 23, 2019
Published electronically: July 8, 2019
Additional Notes: The first author was supported by the Italian MIUR Project PRIN 2010–2011 “Geometria delle varietà algebriche” and by GNSAGA of INdAM. He also acknowledges the MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome “Tor Vergata”, CUP E83C18000100006.
The authors were members of project FOSICAV, which received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 652782.
Communicated by: Rachel Pries
Article copyright: © Copyright 2019 American Mathematical Society