On the period of Li, Pertusi, and Zhao’s symplectic variety

Abstract

We extend classical results of Perego and Rapagnetta on moduli spaces of sheaves of type OG10 to moduli spaces of Bridgeland semistable objects on the Kuznetsov component of a cubic fourfold. In particular, we determine the period of this class of varieties and use it to understand when they become birational to moduli spaces of sheaves on a K3 surface.

On the Hilbert function of Artinian local complete intersections of codimension three

“…The following two problems have very different formulations, but come from the common motivation in enumerative geometry [98,106]. (The following problem has been solved [50] while the present paper was in review.) (Solved) problem XXV.…”

“…The answer is affirmative when Theorem 2] and more generally for ideals I homogeneous with respect to the standard N-grading (and even some nonstandard gradings), see [111]. While this list was in review, a negative answer to the question in Problem XXV was given by Giovenzana-Giovenzana-Graffeo-Lella [50]; it is striking that their example has degree only d = If true, this would imply that Hilb d (A 3 ) is generically reduced, see [117]. In general, the positive answer would restrict the possible singularities of this Hilbert scheme.…”

O’Grady tenfolds as moduli spaces of sheaves

“…Later, we consider the ihs manifold of OG10 type 𝑋 𝑌 , defined by Li, Pertusi and Zhao (LPZ), which is associated with a smooth cubic fourfold Y [29]. We are able to provide a purely lattice-theoretic characterization for 𝑋 𝑌 to be birational to a moduli space of sheaves on a (possibly twisted) K3 surface, providing a new proof of [15,Theorem 3.2].…”