Interesting Esoterica

38406501359372282063949 & all that: Monodromy of Fano Problems

Article by Sachi Hashimoto and Borys Kadets
  • Published in 2020
  • Added on
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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BibTeX entry

@article{38406501359372282063949allthatMonodromyofFanoProblems,
	title = {38406501359372282063949 {\&} all that: Monodromy of Fano Problems},
	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){\$}.},
	url = {http://arxiv.org/abs/2002.04580v1 http://arxiv.org/pdf/2002.04580v1},
	year = 2020,
	author = {Sachi Hashimoto and Borys Kadets},
	comment = {},
	urldate = {2020-05-06},
	archivePrefix = {arXiv},
	eprint = {2002.04580},
	primaryClass = {math.AG},
	collections = {attention-grabbing-titles,combinatorics,integerology}
}