# Mukai's program for curves on a K3 surface

@article{Arbarello2013MukaisPF, title={Mukai's program for curves on a K3 surface}, author={Enrico Arbarello and Andrea Bruno and Edoardo Sernesi}, journal={arXiv: Algebraic Geometry}, year={2013} }

Let C be a general element in the locus of curves in M_g lying on some K3 surface, where g is congruent to 3 mod 4 and greater than or equal to 15. Following Mukai's ideas, we show how to reconstruct the K3 surface as a Fourier-Mukai transform of a Brill-Noether locus of rank two vector bundles on C.

## 23 Citations

Mukai’s program (reconstructing a K3 surface from a curve) via wall-crossing

- Mathematics
- 2017

Abstract Let C be a curve of genus g=11{g=11} or g≥13{g\geq 13} on a K3 surface whose Picard group is generated by the curve class [C]{[C]}. We use wall-crossing with respect to Bridgeland stability…

Embedding pointed curves in K3 surfaces

- Mathematics
- 2013

We analyze morphisms from pointed curves to K3 surfaces with a distinguished rational curve, such that the marked points are taken to the rational curve, perhaps with specified cross ratios. This…

Maximal variation of curves on K3 surfaces

- Mathematics
- 2021

We prove that curves in a non-primitive, base point free, ample linear system on a K3 surface have maximal variation. The result is deduced from general restriction theorems applied to the tangent…

Solvability of curves on surfaces

- Mathematics
- 2017

In this article, we study subloci of solvable curves in $\mathcal{M}_g$ which are contained in either a K3-surface or a quadric or a cubic surface. We give a bound on the dimension of such subloci.…

Rank two vector bundles on polarised Halphen surfaces and the Gauss-Wahl map for du Val curves

- Mathematics
- 2017

A genus-g du Val curve is a degree-3g plane curve having 8 points of multiplicity g, one point of multiplicity g-1, and no other singularity. We prove that the corank of the Gauss-Wahl map of a…

On the Brill-Noether loci of a curve embedded in a K3 surface

- Mathematics
- 2018

We slightly extend a previous result concerning the injectivity of a map of moduli spaces and we use this result to construct curves whose Brill-Noether loci have unexpected dimension.

Curves on surfaces with trivial canonical bundle

- Mathematics
- 2018

We survey some results concerning Severi varieties and variation in moduli of curves lying on K3 surfaces or on abelian surfaces. A number of open problems is listed and some work in progress is…

Moduli of curves on Enriques surfaces

- Mathematics
- 2019

We compute the number of moduli of all irreducible components of the moduli space of smooth curves on Enriques surfaces. In most cases, the moduli maps to the moduli space of Prym curves are…

On hyperplane sections of K 3 surfaces

- 2017

Let C be a Brill–Noether–Petri curve of genus g > 12. We prove that C lies on a polarised K3 surface, or on a limit thereof, if and only if the Gauss–Wahl map for C is not surjective. The proof is…

On hyperplane sections of K3 surfaces

- Mathematics
- 2015

Let C be a Brill-Noether-Petri curve of genus g\geq 12. We prove that C lies on a polarized K3 surface, or on a limit thereof, if and only if the Gauss-Wahl map for C is not surjective. The proof is…

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