Computing moduli spaces for space curve singularities

A Moduli Scheme of Embedded Curve Singularities

A central problem in Algebraic Geometry is the classification of several isomorphism classes of objects by considering their deformations and studying the naturally related moduli problems, see [33], [34]. This general strategy has also been applied to singularities. Some classes of singularities with fixed numerical invariants are studied from the moduli point of view, i.e. proving the existen...

Computing instanton numbers of curve singularities

We start with any polynomial p(x, y) defining a plane curve with singularity at 0 ∈ C. Let π: C̃ → C denote the blow-up of C at the origin and let j be a positive integer. The data (j, p) determines a holomorphic bundle E(j, p) on C̃ with splitting type j and extension class p. We then algorithmically compute numerical invariants of the bundle E(j, p) and use them as invariants of the curve. A co...

Kähler Moduli Space for a D-brane at Orbifold Singularities

We develop a method to analyze systematically the configuration space of a Dbrane localized at the orbifold singular point of a Calabi–Yau d-fold of the form Cd/Γ using the theory of toric quotients. This approach elucidates the structure of the Kähler moduli space associated with the problem. As an application, we compute the toric data of the Γ-Hilbert scheme.

Moduli Spaces of Semiquasihomogeneous Singularities with Fixed Principal Part

Moduli Spaces of Hyperelliptic Curves with a and D Singularities

We introduce moduli spaces of quasi-admissible hyperelliptic covers with at worst A and D singularities. Stability conditions for these moduli problems depend on two parameters describing allowable singularities. At the extreme values of the parameters, we obtain the stacks TAn and TDn of stable limits of An and Dn singularities, as well as the quotients of the miniversal deformation spaces of ...