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...
Abstract A generalised pair is roughly a pair together with a nef divisor on a birational model. The theory of generalized pairs plays an important role in various aspects of birational geometry, such as the proof of the Borisov-Alexeev-Borisov conjecture. In this talk, I will discuss our recent works on the Kodaira vanishing theorem and the Kawamata-Viehweg vanishing theorem for lc generalized...
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