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arXiv · 2002.04580

38406501359372282063949 & all that: Monodromy of Fano Problems

Sachi Hashimoto·Borys Kadets
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Abstract

A Fano problem is an enumerative problem of counting $r$-dimensional linear subspaces on a complete intersection in $\mathbb{P}^n$ over a field of arbitrary characteristic, whenever the corresponding Fano scheme is finite. A classical example is enumerating lines on a cubic surface. We study the monodromy of finite Fano schemes $F_{r}(X)$ as the complete intersection $X$ varies. We prove that the monodromy group is either symmetric or alternating in most cases. In the exceptional cases, the monodromy group is one of the Weyl groups $W(E_6)$ or $W(D_k)$.

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Sachi Hashimoto, Borys Kadets. 2020-02-11. 38406501359372282063949 & all that: Monodromy of Fano Problems. https://doi.org/10.1093/imrn/rnaa275

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