@article {doi:10.1142/S0129167X18500076, title = {Framed symplectic sheaves on surfaces}, journal = {International Journal of Mathematics}, volume = {29}, number = {01}, year = {2018}, pages = {1850007}, abstract = {

A framed symplectic sheaf on a smooth projective surface $X$ is a torsion-free sheaf $E$ together with a trivialization on a divisor $D \subset X$ and a morphism $\Lambda^2 E \rightarrow \mathcal{O}_X$ satisfying some additional conditions. We construct a moduli space for framed symplectic sheaves on a surface, and present a detailed study for $X =\mathbb{P}_\mathbb{C}^2$. In this case, the moduli space is irreducible and admits an ADHM-type description and a birational proper map onto the space of framed symplectic ideal instantons.

}, doi = {10.1142/S0129167X18500076}, url = {https://doi.org/10.1142/S0129167X18500076}, author = {Jacopo Vittorio Scalise} } @mastersthesis {2016, title = {Frames symplectic sheaves on surfaces and their ADHM data}, year = {2016}, school = {SISSA}, abstract = {This dissertation is centered on the moduli space of what we call framed symplectic sheaves on a surface, compactifying the corresponding moduli space of framed principal SP-bundles. It contains the construction of the moduli space, which is carried out for every smooth projective surface X with a big and nef framing divisor, and a study of its deformation theory. We also develop an in-depth analysis of the examples X = P2 and X = Blp (P2 ), showing that the corresponding moduli spaces enjoy an ADHM-type description. In the former case, we prove irreducibility of the space and exhibit a relation with the space of framed ideal instantons on S4 in type C.}, keywords = {moduli spaces}, author = {Jacopo Vittorio Scalise} }