Cycle-valued quasi-modular forms on Kontsevich space

Abstract: On a general rational elliptic surface (fibered over $\mathbb{P}^1$), the number of sections of height $n$ is equal to the coefficient of the Eisenstein series $E_4(q)$ at order $n+1$. I will describe a conjectural generalization of this fact, which associates to any smooth projective variety a quasi-modular form valued in the Chow group of its Kontsevich moduli space. The proof is in progress.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

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