Quantum cohomology of the odd symplectic Grassmannian of lines

Details Quantum cohomology of the odd symplectic Grassmannian of lines Quantum cohomology of the odd symplectic Grassmannian of lines

2010-12-20

arxiv.org/abs/1012.4257v2

Mathematics

Algebraic Geometry

25 pages, proof in section 2.1 simplified, proof of the existence of a full exceptional collection for the derived category IG

Scientific paper

Odd symplectic Grassmannians are a generalization of symplectic Grassmannians to odd-dimensional spaces. Here we compute the classical and quantum cohomology of the odd symplectic Grassmannian of lines. Although these varieties are non homogeneous, we obtain Pieri and Giambelli formulas that are very similar to the symplectic case. We notice that their quantum cohomology is semi-simple, which enables us to check Dubrovin's conjecture for this case.

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