@mastersthesis {32138,
	title = {Vector Bundles on Non-K{\"a}hler Elliptic Surfaces},
	year = {2023},
	type = {PhD thesis},
	abstract = {<p>
	This thesis studies two problems relating to moduli spaces of vector bundles on non-K{\"a}hler elliptic surfaces. The first project involves the holomorphic symplectic structure on smooth and compact moduli spaces of sheaves on Kodaira surfaces. We show that these moduli spaces are neither K{\"a}hler nor simply connected. Comparing \&nbsp;to other known examples of compact holomorphic symplectic manifolds, this shows that if the moduli spaces are deformation equivalent to a known example, then they are Douady spaces of points on a Kodaira surface.\&nbsp;
</p>

<p>
	The second problem deals with the interplay between singularities of moduli spaces of rank-2 vector bundles and existence of stable Vafa--Witten bundles on non-K{\"a}hler elliptic surfaces. By constructing a Vafa--Witten bundle in each filtrable Chern class of the elliptic surface when the base has genus $g\geq 2$, we show that such a moduli space is smooth as a ringed space if and only if every bundle in the moduli space is irreducible.
</p>
},
	author = {Eric Boulter}
}
