1,399 research outputs found
Vector Fields, Invariant Varieties and Linear Systems
We investigate the interplay between invariant varieties of vector fields and
the inflection locus of linear systems with respect to the vector field. Among
the consequences of such investigation we obtain a computational criteria for
the existence of rational first integrals of a given degree, bounds for the
number of first integrals on families of vector fields and a generalization of
Darboux's criteria. We also provide a new proof of Gomez-Mont's result on
foliations with all leaves algebraic.Comment: 15 pages, Late
Transversely projective foliations on surfaces: existence of normal forms and prescription of the monodromy
We introduce a notion of normal form for transversely projective structures
of singular foliations on complex manifolds. Our first main result says that
this normal form exists and is unique when ambient space is two-dimensional.
From this result one obtains a natural way to produce invariants for
transversely projective foliations on surfaces. Our second main result says
that on projective surfaces one can construct singular transversely projective
foliations with prescribed monodromy
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