AbstractIt is well-known that any plane polygon can be decomposed along its diagonals into flat triangles. The analog does not hold for spherical polygons. We prove that any compact surface with constant positive curvature and conical singularities can be decomposed into irreducible components of standard shape, glued along geodesic arcs connecting conical singularities. The irreducible compone...
AbstractWe discuss the enumerative geometry of moduli spaces of sheaves with 2 dimensional support on K3 surfaces in K3-fibered threefolds and 4 folds. The reason to study such specific geometric setups is that these often provide computable invariants which govern deep information about geometry of moduli spaces of solutions to N=2 Super Yang-Mills theory on K3 surfaces, when the base surface ...