Frobenius splittings were introduced by V. B. Mehta and A. Ramanathan in  and refined further by S. Ramanan and Ramanathan in . Frobenius splittings have proven to be a amazingly effective when they apply. Proofs involving Frobenius splittings tend to be very efficient. Other methods usually require a much more detailed knowledge of the object under study. For instance, while showing that the intersection of one union of Schubert varieties with another union of Schubert varieties is reduced, one does not need to know where that intersection is situated, let alone what it looks like exactly.
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