00812nas a2200133   4500008004100000245006300041210006200104260003000166520036300196100001600559700002600575700002600601856005100627       2013                        en  d00aSymplectic instanton bundles on P3 and 't Hooft instantons0 aSymplectic instanton bundles on P3 and t Hooft instantons  barXiv:1312.5554 [math.AG]3 aWe introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus $I^*_{n,r}$ of tame symplectic instantons is irreducible and has the expected dimension, equal to $4n(r+1)-r(2r+1)$. The proof is inherently based on a relation between the spaces $I^*_{n,r}$ and the moduli spaces of 't Hooft instantons.1 aBruzzo, Ugo1 aMarkushevich, Dimitri1 aTikhomirov, Alexander  uhttp://urania.sissa.it/xmlui/handle/1963/3448600979nas a2200133   4500008004100000245010200041210006900143260001000212520051900222100001600741700002600757700002600783856003600809       2012                        en  d00aModuli of symplectic instanton vector bundles of higher rank on  projective space $\\mathbb{P}^3$0 aModuli of symplectic instanton vector bundles of higher rank on   bSISSA3 aSymplectic instanton vector bundles on the projective space $\\mathbb{P}^3$ constitute a natural generalization of mathematical instantons of rank 2. We study the moduli space $I_{n,r}$ of rank-$2r$ symplectic instanton vector bundles on $\\mathbb{P}^3$ with $r\\ge2$ and second Chern class $n\\ge r,\\ n\\equiv r({\\rm mod}2)$. We give an explicit construction of an irreducible component $I^*_{n,r}$ of this space for each such value of $n$ and show that $I^*_{n,r}$ has the expected dimension $4n(r+1)-r(2r+1)$.1 aBruzzo, Ugo1 aMarkushevich, Dimitri1 aTikhomirov, Alexander  uhttp://hdl.handle.net/1963/465601011nas a2200121   4500008004300000245008300043210006900126520059000195100001600785700002600801700002600827856003600853       2010                        en_Ud  00aUhlenbeck-Donaldson compactification for framed sheaves on projective surfaces0 aUhlenbeckDonaldson compactification for framed sheaves on projec3 aWe construct a compactification $M^{\\\\mu ss}$ of the Uhlenbeck-Donaldson type for the moduli space of slope stable framed bundles. This is a kind of a moduli space of slope semistable framed sheaves. We show that there exists a projective morphism $\\\\gamma \\\\colon M^s \\\\to M^{\\\\mu ss}$, where $M^s$ is the moduli space of S-equivalence classes of Gieseker-semistable framed sheaves. The space $M^{\\\\mu ss}$ has a natural set-theoretic stratification which allows one, via a Hitchin-Kobayashi correspondence, to compare it with the moduli spaces of framed ideal instantons.1 aBruzzo, Ugo1 aMarkushevich, Dimitri1 aTikhomirov, Alexander  uhttp://hdl.handle.net/1963/4049