In the paper, we study the GIT construction of the moduli space of Chow semistable curves of genus 4 in P3. By using the GIT method developed by Mumford and a deformation theoretic argument, we give a modular description of this moduli space. We classify Chow stable or Chow semistable curves when they are irreducible or nonreduced. Then we work out the case when a curve has two components. Our ...

For any moduli space of stable representations of quivers, certain smooth varieties, compactifying projective space fibrations over the moduli space, are constructed. The boundary of this compactification is analyzed. Explicit formulas for the Betti numbers of the smooth models are derived. In the case of moduli of simple representations, explicit cell decompositions of the smooth models are co...

A bstract It was recently suggested that certain UV-completable supersymmetric actions can be characterized by the solutions to an auxiliary non-linear sigma-model with special asymptotic boundary conditions. The space-time of this is scalar field space these effective theories while target a coset space. We study without any reference potentially underlying geometric description. Using hologra...

We propose a method of computing the α corrections to the moduli space of hypermultiplets of N = 2 four-dimensional vacua resulting from compactifications of heterotic strings on K3 × T . The method is based on relating the hypermultiplet moduli space of the original model to the vector multiplet moduli space of the ”mirror” one which can be computed exactly due to Heterotic/Type II duality. We...

We provide an M theory interpretation of the recently discovered N=8 supersymmetric Chern-Simons theory with SO(4) gauge symmetry. The theory is argued to describe two membranes moving in the orbifold R8/Z2. At level k=1 and k=2, the classical moduli space M coincides with the infrared moduli space of SO(4) and SO(5) super Yang-Mills theory, respectively. For higher Chern-Simons level, the modu...