TY - RPRT
T1 - Symplectic instanton bundles on P3 and 't Hooft instantons
Y1 - 2013
A1 - Ugo Bruzzo
A1 - Dimitri Markushevich
A1 - Alexander Tikhomirov
AB - We 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.
PB - arXiv:1312.5554 [math.AG]
UR - http://urania.sissa.it/xmlui/handle/1963/34486
N1 - This preprint has been published with the title "Moduli of symplectic instanton vector bundles of higher rank on projective space P-3 " in CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, Volume: 10, issue 4, Augst 2012, pages 1232-1245.
U1 - 34675
U2 - Mathematics
U4 - 1
U5 - MAT/03
ER -
TY - JOUR
T1 - Moduli of symplectic instanton vector bundles of higher rank on projective space $\\mathbbP^3$
JF - Central European Journal of Mathematics 10, nr. 4 (2012) 1232
Y1 - 2012
A1 - Ugo Bruzzo
A1 - Dimitri Markushevich
A1 - Alexander Tikhomirov
AB - Symplectic 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 $4n(r+1)-r(2r+1)$.
PB - SISSA
UR - http://hdl.handle.net/1963/4656
N1 - 14 pages
U1 - 4406
U2 - Mathematics
U3 - Mathematical Physics
U4 - -1
ER -
TY - JOUR
T1 - Moduli of framed sheaves on projective surfaces
JF - Doc. Math. 16 (2011) 399-410
Y1 - 2011
A1 - Ugo Bruzzo
A1 - Dimitri Markushevich
AB - We 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.
PB - Documenta Mathematica
UR - http://hdl.handle.net/1963/5126
U1 - 4942
U2 - Mathematics
U3 - Mathematical Physics
U4 - -1
ER -
TY - RPRT
T1 - Uhlenbeck-Donaldson compactification for framed sheaves on projective surfaces
Y1 - 2010
A1 - Ugo Bruzzo
A1 - Dimitri Markushevich
A1 - Alexander Tikhomirov
AB - We 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.
UR - http://hdl.handle.net/1963/4049
U1 - 353
U2 - Mathematics
U3 - Mathematical Physics
ER -