For a simple, rigid vector bundle F on a Calabi-Yau 3-fold Y, we construct a symmetric obstruction theory on the Quot scheme Quot(Y) (F, n), and we solve the associated enumerative theory. We discuss the case of other 3-folds. Exploiting the critical structure on the local model Quot(A3)(O-circle plus r,n), we construct a virtual motive (in the sense of Behrend-Bryan-Szendroi) for Quot(Y) (F, n) for an arbitrary vector bundle F on a smooth 3-fold Y. We compute the associated motivic partition function. We obtain new examples of higher rank (motivic) Donaldson-Thomas invariants. (C) 2020 Elsevier Inc. All rights reserved.

Virtual classes and virtual motives of Quot schemes on threefolds / Ricolfi, Andrea T.. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 369:(2020), pp. 1-32. [10.1016/j.aim.2020.107182]

Virtual classes and virtual motives of Quot schemes on threefolds

Ricolfi, Andrea T.
2020-01-01

Abstract

For a simple, rigid vector bundle F on a Calabi-Yau 3-fold Y, we construct a symmetric obstruction theory on the Quot scheme Quot(Y) (F, n), and we solve the associated enumerative theory. We discuss the case of other 3-folds. Exploiting the critical structure on the local model Quot(A3)(O-circle plus r,n), we construct a virtual motive (in the sense of Behrend-Bryan-Szendroi) for Quot(Y) (F, n) for an arbitrary vector bundle F on a smooth 3-fold Y. We compute the associated motivic partition function. We obtain new examples of higher rank (motivic) Donaldson-Thomas invariants. (C) 2020 Elsevier Inc. All rights reserved.
2020
369
1
32
107182
https://www.sciencedirect.com/science/article/abs/pii/S0001870820302085?dgcid=author
https://arxiv.org/abs/1906.02557
Ricolfi, Andrea T.
File in questo prodotto:
File Dimensione Formato  
10. Virtual classes and virtual motives of Quot schemes on threefolds.pdf

non disponibili

Descrizione: pdf editoriale
Tipologia: Versione Editoriale (PDF)
Licenza: Non specificato
Dimensione 560.48 kB
Formato Adobe PDF
560.48 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/135070
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 10
social impact