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# Mathematics > Algebraic Geometry

# Title: 38406501359372282063949 & all that: Monodromy of Fano Problems

(Submitted on 11 Feb 2020 (v1), last revised 22 Nov 2020 (this version, v2))

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 $W(D_k)$.

## Submission history

From: Borys Kadets [view email]**[v1]**Tue, 11 Feb 2020 18:14:31 GMT (20kb)

**[v2]**Sun, 22 Nov 2020 22:33:42 GMT (25kb)

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