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Quantum cohomology of complete intersections

Arnaud Beauville
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Abstract

The quantum cohomology algebra of a projective manifold X is the cohomology H(X,Q) endowed with a different algebra structure, which takes into account the geometry of rational curves in X. We show that this algebra takes a remarkably simple form for complete intersections when the dimension is large enough w.r.t. the degree. As a reward we get a number of surprising enumerative formulas relating lines, conics and twisted cubics on X.

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Arnaud Beauville. 1995-01-17. Quantum cohomology of complete intersections. https://arxiv.org/abs/alg-geom/9501008

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