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Oleksandr Iena

Publications and source records attributed to Oleksandr Iena.

7 recordsLinked to original sources
arXiv2018

An observation on the Poincaré polynomials of moduli spaces of one-dimensional sheaves

We notice that for $0<d\le 6$ the Poincaré polynomial of Simpson moduli space $M_{dm + 1}(\mathbb P_2)$ is divisible by the Poincaré polynomial of the projective space $\mathbb P_{3d-1}$. A somehow regular behaviour of the difference of the Poincaré polynomials of the Hilbert scheme of $\frac{(d-2)(d-1)}{2}$ points on $\mathbb P_2$ and the moduli space of Kronecker modules $N(3; d-2, d-1)$ is noticed for $d=4, 5, 6$.

math.AG↗
arXiv2016

A global description of the fine Simpson moduli space of 1-dimensional sheaves supported on plane quartics

A global description of the fine Simpson moduli spaces of $1$-dimensional sheaves supported on plane quartics is given: we describe the gluing of the Brill-Noether loci described by Drézet and Maican and show that the Simpson moduli space $M=M_{4m\pm 1}(\mathbb P_2)$ is a blow-down of a blow-up of a projective bundle over a smooth moduli space of Kronecker modules. An easy computation of the Poincaré polynomial of $M$ is presented.

math.AG↗
arXiv2016

On the singular sheaves in the fine Simpson moduli spaces of $1$-dimensional sheaves

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 vector bundles (on support).

math.AG↗
arXiv2014

Universal plane curve and moduli spaces of 1-dimensional coherent sheaves

We show that the universal plane curve M of fixed degree d > 2 can be seen as a closed subvariety in a certain Simpson moduli space of 1-dimensional sheaves on a projective plane contained in the stable locus. The universal singular locus coincides with the subvariety of M consisting of sheaves that are not locally free on their support. It turns out that the blow up of M along M' may be naturally seen as a compactification of M_B = M\M' by vector bundles (on support).

math.AG↗