The Moduli Space of 3-Folds with K = 0 may Nevertheless be Irreducible.
The moduli space of commutative algebras of finite rank
The moduli space of rank- commutative algebras equipped with an ordered basis is an affine scheme of finite type over , with geometrically connected fibers. It is smooth if and only if . It is reducible if (and the converse holds, at least if we remove the fibers above and ). The relative dimension of is . The subscheme parameterizing étale algebras is isomorphic to , which is of dimension only . For , there exist algebras that are not limits of étale algebras. The dimension calculations...
The moduli space of totally marked degree two rational maps
A rational map ϕ: ℙ¹ → ℙ¹ along with an ordered list of fixed and critical points is called a totally marked rational map. The space of totally marked degree two rational maps can be parametrized by an affine open subset of (ℙ¹)⁵. We consider the natural action of SL₂ on induced from the action of SL₂ on (ℙ¹)⁵ and prove that the quotient space exists as a scheme. The quotient is isomorphic to a Del Pezzo surface with the isomorphism being defined over ℤ[1/2].
The Moduli spaces of Rank 2 Stable Vector Bundles over Veronesean surfaces.
The Moduli Spaces of Vector Bundles over an Algebraic Curve.
The period map for hypersurface sections of high degree of an arbitrary variety
The Picard group of a coarse moduli space of vector bundles in positive characteristic
Let C be a smooth projective curve over an algebraically closed field of arbitrary characteristic. Let M r,Lss denote the projective coarse moduli scheme of semistable rank r vector bundles over C with fixed determinant L. We prove Pic(M r,Lss) = ℤ, identify the ample generator, and deduce that M r,Lss is locally factorial. In characteristic zero, this has already been proved by Drézet and Narasimhan. The main point of the present note is to circumvent the usual problems with Geometric Invariant...
The Picard Group of a Quasi-Bundle.
The Picard group of the compactification of m...3(0, 2).
The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".
The projectivity of the moduli space of stable curves, II: The stacks M...
The projectivity of the moduli space of stable curves, III: The line bundles on M..., and a proof of the projectivity of M... in characteristic 0.
The rationality of some moduli spaces of plane curves
The role of the Ellingsrud-Strømme construction in the classification of instantons
We review a construction of Ellingsrud-Strømme relating instantons of charge n on the ordinary projective space and theta-characteristics on a plane curve of degree n with some extra-structure.
The scheme of morphisms from an elliptic curve to a Grassmannian
The Second Homology Group of the Mapping Class Group of an Orientable Surface.
The Shafarevich-Tate Conjecture for Pencils of Elliptic Curves on K3 Surfaces.
The Singular Points on the Moduli Spaces for Smooth Curves.
The singularities of Yang-Mills connections for bundles on a surface.
The SL(2, C) - character varieties of torus knots.