Extended Petrov-Semenov's connections

摘要

For a smooth projective quadric X, Alexander Vishik introduced the notion of connections. He discovered connections arising from the splitting pattern of X as well as the so-called excellent connections. Recently, Victor Petrov and Nikita Semenov found new connections arising from the J-invariantJ(X), which is a layer of the elementary discrete invariantED(X), both further Vishik's inventions. In this note, we give a new proof for Peterov-Semenov's connections and extend them to the remaining layers of ED(X). Also, we briefly discuss connections on nonsmooth quadrics.