On the semi-simplicity of the quantum cohomology algebras of complete intersections
نویسندگان
چکیده
In this short note, we study the semi-simplicity of the quantum cohomology algebras of smooth Fano complete intersections in projective space. Let V be a smooth Fano manifold with a symplectic form ω. The quantum cohomology on V is the cohomology H(V,Z{H2(V )}) with a ring structure defined by the GW-invariants. The Novikov ring Z{H2(V )} can be described as follows: choose a basis q1, · · · , qs of H2(V,Z), we identify the monomial q d = q1 1 · · · q ds s with the sum ∑s i=1 diqi. This turns H2(V ) into a multiplicative ring, i.e., q d · q ′ = q ′ . This multiplicative ring has a natural grading defined by deg(q) = 2c1(V )( ∑
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