For a simple, simply connected, complex group G, we prove the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points.
Algebraic Geometry High Energy Physics - Theory Differential Geometry Representation Theory Primary: 14H60, 32G34, 53D50, Secondary: 81T40, 14F08
By analyzing toric degenerations of the moduli spaces we explain how graph potentials are related to these moduli spaces in the setting of mirror symmetry for Fano varieties.
Algebraic Geometry Geometric Topology Quantum Algebra Symplectic Geometry
We give the first examples of smooth Fano and Calabi-Yau varieties violating the (narrow) canonical strip hypothesis, which concerns the location of the roots of Hilbert polynomials of polarised varieties.
Algebraic Geometry 14J45, 14J32, 14D20