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See detailOn unavoidable families of meromorphic functions
Meyrath, Thierry UL

in Canadian Mathematical Bulletin (in press)

We prove several results on unavoidable families of meromorphic functions. For instance, we give new examples of families of cardinality three that are unavoidable with respect to the set of meromorphic ... [more ▼]

We prove several results on unavoidable families of meromorphic functions. For instance, we give new examples of families of cardinality three that are unavoidable with respect to the set of meromorphic functions on $\C$. We further obtain families consisting of less than three functions that are unavoidable with respect to certain subsets of meromorphic functions. In the other direction, we show that for every meromorphic function $f$, there exists an entire function that avoids $f$ on $\C$. [less ▲]

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See detailOn the singular sheaves in the fine Simpson moduli spaces of 1-dimensional sheaves
Iena, Oleksandr UL; Leytem, Alain UL

in Canadian Mathematical Bulletin (2016)

In the Simpson moduli space $M$ of semi-stable sheaves with Hilbert polynomial $dm-1$ on a projective plane we study the closed subvariety $M'$ of sheaves that are not locally free on their support. We ... [more ▼]

In the Simpson moduli space $M$ of semi-stable sheaves with Hilbert polynomial $dm-1$ on a projective plane we study the closed subvariety $M'$ of sheaves that are not locally free on their support. We show that for $d\ge 4$ it is a singular subvariety of codimension $2$ in $M$. The blow up of $M$ along $M'$ is interpreted as a (partial) modification of $M\setminus M'$ by line bundles (on support). [less ▲]

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