A note on Bridgeland moduli spaces and moduli spaces of sheaves on X14 and Y3

ZHIYU LIU, Shizhuo Zhang

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We study Bridgeland moduli spaces of semistable objects of (−1)-classes and (−4)-classes in the Kuznetsov components on index one prime Fano threefold X4d+2 of degree 4d+2 and index two prime Fano threefold Yd of degree d for d=3,4,5. For every Serre-invariant stability condition on the Kuznetsov components, we show that the moduli spaces of stable objects of (−1)-classes on X4d+2 and Yd are isomorphic. We show that moduli spaces of stable objects of (−1)-classes on X14 are realized by Fano surface C(X) of conics, moduli spaces of semistable sheaves MX(2,1,6) and MX(2,−1,6) and the correspondent moduli spaces on cubic threefold Y3 are realized by moduli spaces of stable vector bundles MbY(2,1,2) and MbY(2,−1,2). We show that moduli spaces of semistable objects of (−4)-classes on Yd are isomorphic to the moduli spaces of instanton sheaves MinstY when d≠1,2, and show that there're open immersions of MinstY into moduli spaces of semistable objects of (−4)-classes when d=1,2. Finally, when d=3,4,5 we show that these moduli spaces are all isomorphic to MssX(2,0,4).
Original languageEnglish
Pages (from-to)803-837
JournalMathematische zeitschrift
Volume302
Early online date20 Jul 2022
DOIs
Publication statusPublished - 31 Oct 2022

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