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/1963/465600841nas a2200121   4500008004100000245005200041210005200093260002600145520047000171100001600641700002600657856003600683       2011                        en  d00aModuli of framed sheaves on projective surfaces0 aModuli of framed sheaves on projective surfaces  bDocumenta Mathematica3 aWe show that there exists a fine moduli space for torsion-free sheaves on a\\r\\nprojective surface, which have a \\\"good framing\\\" on a big and nef divisor. This\\r\\nmoduli space is a quasi-projective scheme. This is accomplished by showing that such framed sheaves may be considered as stable pairs in the sense of\\r\\nHuybrechts and Lehn. We characterize the obstruction to the smoothness of the moduli space, and discuss some examples on rational surfaces.1 aBruzzo, Ugo1 aMarkushevich, Dimitri  uhttp://hdl.handle.net/1963/512601011nas 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