arXiv subjects

Soheyla Feyzbakhsh

Publications and source records attributed to Soheyla Feyzbakhsh.

21 records · Page 2Linked to original sources

arXiv2020

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

Let $C$ be a curve of genus $g \geq 11$ such that $g-1$ is a composite number. Suppose $C$ is on a K3 surface whose Picard group is generated by the curve class $[C]$. We use wall-crossing with respect to Bridgeland stability conditions to generalise Mukai's program to this situation: we show how to reconstruct the K3 surface containing the curve $C$ as a Fourier-Mukai transform of a Brill-Noether locus of vector bundles on $C$.

math.AG↗

arXiv2020

Mukai's Program (reconstructing a K3 surface from a curve) via wall-crossing, II

Let $C$ be a curve on a K3 surface $X$ with Picard group $\mathbb{Z}.[C]$. Mukai's program seeks to recover $X$ from $C$ by exhibiting it as a Fourier-Mukai partner to a Brill-Noether locus of vector bundles on $C$. We use wall-crossing in the space of Bridgeland stability conditions to prove this for genus $\ge14$. This paper deals with the case $g-1$ prime left over from Paper I.

math.AG↗

arXiv2018

Higher rank Clifford indices of curves on a K3 surface

Let $(X,H)$ be a polarized K3 surface with $\mathrm{Pic}(X) = \mathbb Z H$, and let $C\in |H|$ be a smooth curve of genus $g$. We give an upper bound on the dimension of global sections of a semistable vector bundle on $C$. This allows us to compute the higher rank Clifford indices of $C$ with high genus. In particular, when $g\geq r^2\geq 4$, the rank $r$ Clifford index of $C$ can be computed by the restriction of Lazarsfeld-Mukai bundles on $X$ corresponding to line bundles on the curve $C$. This is a generalization of the result by Green and Lazarsfeld for curves on K3 surfaces to higher rank vector bundles. We also apply the same method to the projective plane and show that the rank $r$ Clifford index of a degree $d(\geq 5)$ smooth plane curve is $d-4$, which is the same as the Clifford index of the curve.

math.AG↗