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Moduli of representations of the fundamental group of a smooth projective variety, II . Finite group actions and étale cohomology . A rank theorem for analytic maps between power series spaces . Some groups whose reduced C[*]-algebra is simple . Existence de 1-formes fermées non singulières dans une classe de cohomologie de de Rahm

On globally generated vector bundles on projective spaces

One classifies the globally generated vector bundles on with the first Chern class c1 = 3. The case c1 = 1 is very easy, the case c1 = 2 was done in [42], the case c1 = 3, rank =2 was settled in [21] and the case c1 ≤ 5, rank = 2 in [10]. Our work is based on Serre's theorem relating vector bundles of rank = 2 with codimension 2 lci subschemes and its generalization for higher ranks, considered firstly by Vogelaar in [48].

Globally generated vector bundles on Pn with c1=3

Vector spaces of skew-symmetric matrices of constant rank

We study the irreducible components of the moduli space of instanton sheaves on $\mathbb{P}^3$, that is rank 2 torsion free sheaves $E$ with $c_1(E)=c_3(E)=0$ satisfying $h^1(E(-2))=h^2(E(-2))=0$. In particular, we classify all instanton sheaves with $c_2(E)\le4$, describing all the irreducible components of their moduli space. A key ingredient for our argument is the study of the moduli space ${\mathcal T}(d)$ of stable sheaves on $\mathbb{P}^3$ with Hilbert polynomial $P(t)=d\cdot t$, which contains, as an open subset, the moduli space of rank 0 instanton sheaves of multiplicity $d$; we describe all the irreducible components of ${\mathcal T}(d)$ for $d\le4$.

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Moduli spaces of rank 2 instanton sheaves on the projective space

We investigate the moduli spaces of stable sheaves on a smooth quadric surface with linear Hilbert bipolynomial in some special cases and describe their geometry in terms of the locally free resolution of the sheaves.

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Stable sheaves on a smooth quadric surface with linear Hilbert bipolynomials.

We classify the Ulrich vector bundles of arbitrary rank on smooth projective varieties of minimal degree. In the process, we prove the stability of the sheaves of relative differentials on rational scrolls.

Ulrich bundles on smooth projective varieties of minimal degree

Globally generated vector bundles of rank 2 on a smooth quadric threefold

We investigate the logarithmic bundles associated to arrangements of hypersurfaces with a fixed degree in a smooth projective variety. We then specialize to the case when the variety is a quadric hypersurface and a multiprojective space to prove a Torelli type theorem in some cases.

A torelli-type problem for logarithmic bundles over projective varieties

We classify the Ulrich vector bundles of arbitrary rank on smooth projective varieties of minimal degree In the process, we prove the stability of the sheaves of relative differentials on rational scrolls

Sukmoon Huh

Papers

Stable sheaves on a smooth quadric surface with linear Hilbert bipolynomials.

Ulrich bundles on smooth projective varieties of minimal degree

Globally generated vector bundles of rank 2 on a smooth quadric threefold

A torelli-type problem for logarithmic bundles over projective varieties

Ulrich bundles on smooth projective varieties of minimal degree