On the Number of Irreducible Components of the Moduli Space of Semistable Reflexive Rank 2 Sheaves on the Projective Space

In 2017, Jardim, Markushevich, and Tikhomirov found a new infinite seriesof irreducible components of the moduli space of semistable nonlocally free reflexiverank 2 sheaves on the complex three-dimensional projective space with even first Chernclass whose second and third Chern classes can be represented as polynomials of a specialform in three integer variables. A similar series for reflexive sheaves with odd firstChern class was found in 2022 by Almeida, Jardim, and Tikhomirov. In thisarticle, we prove the uniqueness of the components in these series for the Chern classesrepresented by the above-mentioned polynomials and propose some criteria for the existenceof these components. We formulate a conjecture on the number of components of the modulispace of stable rank 2 sheaves on a three-dimensional projective space such thatthe generic points of these components correspond to isomorphism classes of reflexivesheaves with fixed Chern classes defined by the same polynomials.