5 problems

Carrell's conjecture. A smooth projective variety that admits a holomorphic vector field with exactly one zero is rational.

Equivalence conjecture. The following statements are equivalent:

Consider the singular points $z_j$ of the vector field studied in the source, and the periodic domain associated with each singular point. For every $j>1$, consider the boundary of…

Consider the vector-field family denoted by … , $k-1$ open sets are sufficient, and these domains are exactly those to which the study can be reduced using the symmetries of the sy…

Let $k\geq 2$ and consider the family of vector fields … A single open set with slits should be sufficient to describe this family using the periodgon description, whereas two open…