Madeeha Khalid

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In graph pegging, we view each vertex of a graph as a hole into which a peg can be placed, with checker-like " pegging moves " allowed. Motivated by well-studied questions in graph pebbling, we introduce two pegging quantities. The pegging number (respectively, the optimal pegging number) of a graph is the minimum number of pegs such that for every(More)
We consider relationships between families of K3 surfaces, in the context of string theory. An important ingredient of string theory also of interest in algebraic geometry is T-duality. Donagi and Pantev [DP] have extended the original duality on genus one fibred K3 surfaces with a section to the case of any genus one fibration, via a Fourier-Mukai(More)
Let X be a K3 surface of degree 8 in P 5 with hyperplane section H. Given X we can associate to it another K3 surface M which is a double cover of P 2 ramified on a sextic curve C. We study the relation between the moduli space M = M H (2, H, 2) and M. We build on previous work of Mukai and others, giving conditions and examples where M is fine, compact,(More)
We study Lagrangian points on smooth holomorphic curves in TP 1 equipped with a natural neutral Kähler structure, and prove that they must form real curves. By virtue of the identification of TP 1 with the space L(E 3) of oriented affine lines in Euclidean 3-space E 3 , these Lagrangian curves give rise to ruled surfaces in E 3 , which we prove have zero(More)
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