## On the irreducibility of Severi varieties on $K3$ surfaces

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- by C. Ciliberto and Th. Dedieu PDF
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**147**(2019), 4233-4244 Request permission

## 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.## References

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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
- Email: cilibert@mat.uniroma2.it
**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
- Email: thomas.dedieu@math.univ-toulouse.fr
- 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
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**147**(2019), 4233-4244 - MSC (2010): Primary 14H15, 14J28
- DOI: https://doi.org/10.1090/proc/14559
- MathSciNet review: 4002538