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

Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA

https://doi.org/10.1142/S0129167X21500981Cited by:0 (Source: Crossref)

Abstract

For a smooth projective variety $X$ $X$ , we study analogs of Quot schemes using hearts of non-standard $t$ $t$ -structures of $D^{b} (Coh (X))$ $D^{b} (Coh (X))$ . The technical framework uses families of $t$ $t$ -structures as studied in A. Bayer, M. Lahoz, E. Macrì, H. Nuer, A. Perry and P. Stellari, Stability conditions in families, preprint (2019), 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 M. Thaddeus, Stable pairs, linear systems and the Verlinde formula, Invent. Math. 117(2) (1994) 317–353; D. Huybrechts and M. Lehn, Stable pairs on curves and surfaces, J. Algebraic Geom. 4(1) (1995) 67–104, as instances of Quot schemes.

Communicated by Oscar Garcia-Prada

Keywords:

AMSC: 18G80, 14F08, 14D20

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