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Series: Algebra Seminar

TBA

Series: Algebra Seminar

TBD.

Series: Algebra Seminar

TBA

Series: Algebra Seminar

TBA

Series: Algebra Seminar

Series: Algebra Seminar

Let X be a degree d curve in the projective space P^r. A general hyperplane H intersects X at d distinct points; varying H defines a monodromy action on X∩H. The resulting permutation group G is the sectional monodromy group of X. When the ground field has characteristic zero the group G is known to be the full symmetric group.By work of Harris, if G contains the alternating group, then X satisfies a strengthened Castelnuovo's inequality (relating the degree and the genus of X).The talk is concerned with sectional monodromy groups in positive characteristic. I will describe all nonstrange nondegenerate curves in projective spaces of dimension r>2. for which G is not symmetric or alternating. For a particular family of plane curves. I will compute the sectional monodromy groups and thus answer an old question on Galois groups of generic trinomials.

Series: Algebra Seminar

Series: Algebra Seminar

TBA

Series: Algebra Seminar

TBA

Series: Algebra Seminar

The conjectures of Green—Griffths—Lang predict the precise
interplay between different notions of hyperbolicity: Brody hyperbolic,
arithmetically hyperbolic, Kobayashi hyperbolic, algebraically
hyperbolic, groupless,
and more. In his thesis (1993), W.~Cherry defined a notion of
non-Archimedean hyperbolicity; however, his definition does not seem to
be the ``’correct’ version, as it does not mirror complex
hyperbolicity.
In recent work, A.~Javanpeykar and A.~Vezzani introduced a new
non-Archimedean notion of hyperbolicity, which ameliorates this issue,
and also stated a non-Archimedean variant of the Green—Griffths—Lang
conjecture.
In this talk, I will discuss
complex and non-Archimedean notions of hyperbolicity as well as some
recent progress on the non-Archimedean Green—Griffths—Lang conjecture.
This is joint work with Ariyan Javanpeykar (Mainz)
and Alberto Vezzani (Paris 13).