38406501359372282063949 and All That: Monodromy of Fano Problems

Sachi Hashimoto; Borys Kadets

doi:10.1093/imrn/rnaa275

38406501359372282063949 and All That: Monodromy of Fano Problems

Sachi Hashimoto
, Borys Kadets^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

A Fano problem is an enumerative problem of counting r-dimensional linear subspaces on a complete intersection in Pn 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 Fr(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(E6) or W(Dk).

Original language	English
Pages (from-to)	3349-3370
Number of pages	22
Journal	International Mathematics Research Notices
Volume	2022
Issue number	5
DOIs	https://doi.org/10.1093/imrn/rnaa275
State	Published - 1 Mar 2022
Externally published	Yes

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© 2020 The Author(s) 2020. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected].

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abstract = "A Fano problem is an enumerative problem of counting r-dimensional linear subspaces on a complete intersection in Pn 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 Fr(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(E6) or W(Dk).",

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N2 - A Fano problem is an enumerative problem of counting r-dimensional linear subspaces on a complete intersection in Pn 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 Fr(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(E6) or W(Dk).

AB - A Fano problem is an enumerative problem of counting r-dimensional linear subspaces on a complete intersection in Pn 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 Fr(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(E6) or W(Dk).

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38406501359372282063949 and All That: Monodromy of Fano Problems

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