Новая компонента схемы модулей $\textrm{M}_{\mathbb{P}^3}(2;-1,4,0)$ полустабильных пучков ранга два на проективном пространстве $\mathbb{P}^3$
Новая компонента схемы модулей $\textrm{M}_{\mathbb{P}^3}(2;-1,4,0)$ полустабильных пучков ранга два на проективном пространстве $\mathbb{P}^3$
Аннотация:
In this paper we study the Gieseker-Maruyama moduli space
$\textrm{M}_{\mathbb{P}^3}(2;-1,4,0)$ of semistable coherent sheaves of
rank two with Chern classes $c_1=-1,\ c_2=4,\ c_3=0$ on the
projective space $\mathbb{P}^3$. To date, only two irreducible components of this space have been known, and their general
points are locally free sheaves. In this paper we find and describe a new irreducible component of the space $\textrm{M}_{\mathbb{P}^3}(2;-1,4,0)$, a general point of which is a sheaf
with the singularity at a disjoint union of a pair of lines and
a pair of points. We prove that this component has the expected
dimension 27 and is generically reduced as a scheme.
Ключевые слова: (semi)stable coherent sheaves, rank two sheaves, moduli space of semistable sheaves.