Corpus ID: 237581212

Severi varieties on blow--ups of the symmetric square of an elliptic curve

@inproceedings{Ciliberto2021SeveriVO,
  title={Severi varieties on blow--ups of the symmetric square of an elliptic curve},
  author={Ciro Ciliberto and Thomas Dedieu and Concettina Galati and Andreas Leopold Knutsen},
  year={2021}
}
We prove that certain Severi varieties of nodal curves of positive genus on general blow–ups of the twofold symmetric product of a general elliptic curve are non– empty and smooth of the expected dimension. This result, besides its intrinsic value, is an important preliminary step for the proof of nonemptiness of Severi varieties on general Enriques surfaces in [7]. 

References

SHOWING 1-10 OF 28 REFERENCES
Geometry of families of nodal curves on the blown-up projective plane
Let P2r be the projective plane blown up at r generic points. Denote by E0; E1; : : : ; Er the strict transform of a generic straight line on P2 and the exceptional divisors of the blown-up points onExpand
On Severi Varieties on Hirzebruch Surfaces
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.
Geometry of logarithmic Severi varieties at a general point
This is a set of notes based on the results of Caporaso and Harris' [3, §2], taken on the occasion of the seminar Degenerazioni e enumerazione di curve su una superficie run at Roma "Tor Vergata"Expand
Severi varieties and branch curves of abelian surfaces of type (1,3)
Let (A,L) be a principally polarized abelian surface of type (1,3). The linear system |L| defines a 6:1 covering of A onto P2, branched along a curve B of degree 18 in P2. The main result of theExpand
The Severi problem for abelian surfaces in the primitive case
  • Adrian Zahariuc
  • Mathematics
  • Journal de Mathématiques Pures et Appliquées
  • 2021
We prove that the irreducible components of primitive class Severi varieties of general abelian surfaces are completely determined by the maximal factorization through an isogeny of the maps from theExpand
On the Symmetric Product of a Curve with General Moduli
We study the problem of describing the cone of the effective divisors in the second symmetric product of a curve with general moduli using a degeneration to a rational g-nodal curve.
A Note on Severi Varieties of Nodal Curves on Enriques Surfaces
Let |L| be a linear system on a smooth complex Enriques surface S whose general member is a smooth and irreducible curve of genus p, with L2 > 0, and let V|L|,δ(S) be the Severi variety ofExpand
Counting plane curves of any genus
We obtain a recursive formula answering the following question: How many irreducible, plane curves of degree d and (geometric) genus g pass through 3d-1+g general points in the plane? The formula isExpand
The Severi problem for Hirzebruch surfaces
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.
The Severi Problem for Rational Curves on del Pezzo Surfaces
Let X be a smooth projective surface and choose a curve C on X. Let VC be the set of all irreducible divisors on X linearly equivalent to C whose normalization is a rational curve. The Severi problemExpand
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