Moduli of Prym curves.
Moduli of representations of the fundamental group of a smooth projective variety I
Moduli of representations of the fundamental group of a smooth projective variety II
Moduli of simple Rank-2 sheaves on K3-surfaces.
Moduli of stable sheaves on ruled surfaces and their Picard groups.
Moduli of surfaces of general type with a fibration by genus two curves.
Moduli of symplectic instanton vector bundles of higher rank on projective space ℙ3
Symplectic instanton vector bundles on the projective space ℙ3 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 ℙ3 with r ≥ 2 and second Chern class n ≥ r, n ≡ r (mod 2). 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)...
Moduli of unipotent representations I: foundational topics
With this work and its sequel, Moduli of unipotent representations II, we initiate a study of the finite dimensional algebraic representations of a unipotent group over a field of characteristic zero from the modular point of view. Let be such a group. The stack of all representations of dimension is badly behaved. In this first installment, we introduce a nondegeneracy condition which cuts out a substack which is better behaved, and, in particular, admits a coarse algebraic space, which...
Moduli of Vector Bundles on Curves with Parabolic Structures.
Moduli of vector bundles on projective surfaces: some basic results.
Moduli of Vector Bundles on the Projective Plane.
Moduli reflexiver Garben und Flächen von kleinem Grad in IP4.
Moduli schemes of generically simple Azumaya modules.
Moduli Spaces for Hopf Surfaces.
Moduli spaces for linear differential equations and the Painlevé equations
A systematic construction of isomonodromic families of connections of rank two on the Riemann sphere is obtained by considering the analytic Riemann–Hilbert map , where is a moduli space of connections and , the monodromy space, is a moduli space for analytic data (i.e., ordinary monodromy, Stokes matrices and links). The assumption that the fibres of (i.e., the isomonodromic families) have dimension one, leads to ten moduli spaces . The induced Painlevé equations are computed explicitly....
Moduli Spaces for Real Algebraic Curves and Real Abelian Varieties.
Moduli spaces of covers and the Hurwitz monodromy group.
Moduli spaces of decomposable morphisms of sheaves and quotients by non-reductive groups
We extend the methods of geometric invariant theory to actions of non–reductive groups in the case of homomorphisms between decomposable sheaves whose automorphism groups are non–reductive. Given a linearization of the natural action of the group on Hom(E,F), a homomorphism is called stable if its orbit with respect to the unipotent radical is contained in the stable locus with respect to the natural reductive subgroup of the automorphism group. We encounter effective numerical conditions for...
Moduli spaces of local systems and higher Teichmüller theory
Let G be a split semisimple algebraic group over Q with trivial center. Let S be a compact oriented surface, with or without boundary. We define positive representations of the fundamental group of S to G(R), construct explicitly all positive representations, and prove that they are faithful, discrete, and positive hyperbolic; the moduli space of positive representations is a topologically trivial open domain in the space of all representations. When S have holes, we defined two moduli spaces closely...
Moduli spaces of polarized irreducible symplectic manifolds are not necessarily connected
We show that the moduli space of polarized irreducible symplectic manifolds of -type, of fixed polarization type, is not always connected. This can be derived as a consequence of Eyal Markman’s characterization of polarized parallel-transport operators of -type.