By the Lefschetz hyperplane theorem, if X is a smooth quasi-projective variety and C a general curve section of X then the fundamental group of C surjects onto the fundamental group of X. Here we consider when this property holds for a general member of an arbitrary family of curves that covers X. The most interesting case is families of rational curves.
|Original language||English (US)|
|Title of host publication||Contemporary Mathematics|
|Publisher||American Mathematical Society|
|Number of pages||12|
|State||Published - 2015|
All Science Journal Classification (ASJC) codes