Browsing by Author "Markushevich, Dimitri"

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    Symplectic instanton bundles on P3 and 't Hooft instantons
    (arXiv:1312.5554 [math.AG], 2013-12) Bruzzo, Ugo; Markushevich, Dimitri; Tikhomirov, Alexander; Mathematics
    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.
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    Uhlenbeck-Donaldson compactification for framed sheaves on projective surfaces
    (2010-09-08T08:00:00Z) Bruzzo, Ugo; Markushevich, Dimitri; Tikhomirov, Alexander; Mathematics; Mathematical Physics
    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.