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Results tagged with monodromy
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user 919
14
votes
2
answers
935
views
Non semi-simple monodromy in an algebraic family
of a (edit: projective) family
$f : X \to Y$
of complex algebraic varieties which is a topologically locally trivial fibration in (singular) varieties and such that there exists an $q$ such that the monodromy … Indeed, if $Y = \mathbb{A}^1 \setminus \{ x_1, \dots, x_n \}$ and $f$ is smooth then the monodromy around any $x_i$ will be quasi-unipotent. …
- 6,162
4
votes
Non semi-simple monodromy in an algebraic family
So it seems passerby's example can be modified to give a projective example.
(Thanks for de Cataldo and Migliorini for some of the following. All mistakes are mine.)
Fix $E$ an elliptic curve and …
- 6,162
27
votes
0
answers
953
views
Nearby cycles without a function
Firstly, $\psi_f(\mathbb{Q}_X)$ is a perverse sheaf, and it comes with a monodromy endomorphism $\mu$. I assume that $\mu$ is unipotent. … Secondly, $\psi_f(\mathbb{Q}_X)$ carries a weight filtration $W$, and a deep theorem of Gabber states that the weight filtration agrees with the monodromy filtration. …
- 6,162