Some Quot schemes in tilted hearts and moduli spaces of stable pairs

Abstract

For a smooth projective variety $X$, we study analogs of Quot functors in hearts of non-standard $t$-structures of $D^b(\mathrm{Coh}(X))$. The technical framework is that of families of $t$-structures, as studied in arXiv:1902.08184. We provide several examples and suggest possible directions of further investigation, as we reinterpret moduli spaces of stable pairs, in the sense of Thaddeus (arXiv:alg-geom/9210007) and Huybrechts-Lehn (arXiv:alg-geom/9211001), as instances of Quot schemes.

27 pages, 1 figure. Subsumes results from Chapter 2 of the author's PhD thesis. V2: References updated. V3: final version, to appear in Internat. J. Math. Comments are welcome!

References in corpus (1)

• Moduli spaces on the Kuznetsov component of Fano threefolds of index 2

Cited by in corpus (2)

• A note on the Kuznetsov component of the Veronese double cone
• Multiple cover formulas for K3 geometries, wall-crossing, and Quot schemes