Mathematics – Algebraic Geometry
Scientific paper
2010-09-02
Mathematics
Algebraic Geometry
24 pages
Scientific paper
Let $X$ denote a flag variety of type $A$ or type $C$. We construct a canonical Frobenius splitting of $X \times X$ which vanishes with maximal multiplicty along the diagonal. This way we verify a conjecture by Lakshmibai, Mehta and Parameswaran in type $C$, and obtain a new proof in type $A$. In particular, we obtain a proof of Wahl's conjecture in type $C$, and a new proof in type $A$. We also present certain cohomological consequences.
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