Rigidity and Schofield’s partial tilting conjecture for quiver moduli

Pieter Belmans; Ana-Maria Brecan; Hans Franzen; Gianni Petrella; Markus Reineke

doi:10.5802/jep.312

Rigidity and Schofield’s partial tilting conjecture for quiver moduli
[Rigidité et conjecture de tilting partiel de Schofield pour les espaces de modules de carquois]

Pieter Belmans ¹ ; Ana-Maria Brecan ; Hans Franzen ² ; Gianni Petrella ³ ; Markus Reineke ⁴

¹ Mathematical Institute, Utrecht University, Budapestlaan 6, 3584 CD Utrecht, The Netherlands
² Institute of Mathematics, Paderborn University, Warburger Str. 100, 33098 Paderborn, Germany
³ Department of Mathematics, Université de Luxembourg, 2 Av. de l’Université, 4365, Esch-sur-Alzette, Luxembourg
⁴ Fakultat für Mathematik, Ruhr-Universität Bochum, Universitätsstr. 150, 44780 Bochum, Germany

Journal de l’École polytechnique — Mathématiques, Tome 12 (2025), pp. 1345-1379.

Abstract (VO)
Résumé

We explain how Teleman quantization can be applied to moduli spaces of quiver representations, in order to compute the higher cohomology of the endomorphism bundle of the universal bundle. We use this to prove Schofield’s partial tilting conjecture in many interesting cases, and to show that moduli spaces of quiver representations are often (infinitesimally) rigid as varieties.

Nous expliquons comment la quantification de Teleman peut être appliquée aux espaces de modules de représentations de carquois, afin de calculer la cohomologie supérieure du fibré des endomorphismes du fibré universel. Nous utilisons cela pour démontrer la conjecture de tilting partiel de Schofield dans de nombreux cas intéressants, et pour montrer que les espaces de modules de représentations de carquois sont souvent (infinitésimalement) rigides en tant que variétés.

Reçu le : 2025-02-14
Accepté le : 2025-07-30
Publié le : 2025-09-04

DOI : 10.5802/jep.312

Classification : 14D20, 14F08, 16G20
Keywords: Moduli spaces of quiver representations, Teleman quantization, deformation theory
Mots-clés : Espaces de modules de représentations de carquois, quantification de Teleman, rigidité

Affiliations des auteurs :

Pieter Belmans ¹ ; Ana-Maria Brecan ; Hans Franzen ² ; Gianni Petrella ³ ; Markus Reineke ⁴

¹ Mathematical Institute, Utrecht University, Budapestlaan 6, 3584 CD Utrecht, The Netherlands
² Institute of Mathematics, Paderborn University, Warburger Str. 100, 33098 Paderborn, Germany
³ Department of Mathematics, Université de Luxembourg, 2 Av. de l’Université, 4365, Esch-sur-Alzette, Luxembourg
⁴ Fakultat für Mathematik, Ruhr-Universität Bochum, Universitätsstr. 150, 44780 Bochum, Germany

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Rigidity and {Schofield{\textquoteright}s} partial tilting conjecture for quiver moduli},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
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Pieter Belmans; Ana-Maria Brecan; Hans Franzen; Gianni Petrella; Markus Reineke. Rigidity and Schofield’s partial tilting conjecture for quiver moduli. Journal de l’École polytechnique — Mathématiques, Tome 12 (2025), pp. 1345-1379. doi : 10.5802/jep.312. https://jep.centre-mersenne.org/articles/10.5802/jep.312/

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