00893nas a2200121 4500008004100000245004200041210004200083300001200125490000700137520055100144100003000695856004600725 2018 eng d00aFramed symplectic sheaves on surfaces0 aFramed symplectic sheaves on surfaces a18500070 v293 a
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.
1 aScalise, Jacopo, Vittorio uhttps://doi.org/10.1142/S0129167X1850007601114nas a2200121 4500008004100000245006200041210006200103260001000165520067200175653001800847100003000865856009700895 2016 en d00aFrames symplectic sheaves on surfaces and their ADHM data0 aFrames symplectic sheaves on surfaces and their ADHM data bSISSA3 aThis 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 SPâbundles. 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.10amoduli spaces1 aScalise, Jacopo, Vittorio uhttps://www.math.sissa.it/publication/frames-symplectic-sheaves-surfaces-and-their-adhm-data