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Regular version of the site

Article

Geography and geometry of the moduli spaces of semi-stable rank 2 sheaves on projective space

Matemática Contemporânea. 2020. Vol. 47. P. 301-316.

In this article, we will give a review of recent results on the geography and geometry of the Gieseker-Maruyama moduli scheme M = M (c1 , c2 ) of rank 2 semi-stable coherent sheaves with first Chern class c1 = 0 or −1, second Chern class c2 , and third Chern class 0 on the projective space P3 . We enumerate all currently known irreducible components of M for small values of c2 . We then present constructions of new series of components of M for arbitrary c2 . The problem of connectedness of M and also the problem of rationality of some series of components of M are discussed.