### Sectional monodromy groups of projective curves

- Series
- Algebra Seminar
- Time
- Monday, March 11, 2019 - 12:50 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Borys Kadets – MIT – bkadets@mit.edu

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 non-strange non-degenerate 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.