‘t Hooft bundles on the complete flag threefold and moduli spaces of instantons

In this work we study the moduli spaces of instanton bundles on the flag twistor space $F:=F(0,1,2)$. We stratify them in terms of the minimal twist supporting global sections and we introduce the notion of (special) 't Hooft bundle on $F$. In particular we prove that there exist $\mu$-stable &...

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Bibliographic Details
Authors: Antonelli, Vincenzo, Malaspina, Francesco, Marchesi, Simone, Pons Llopis, Joan
Format: article
Status:Published version
Publication Date:2025
Country:España
Institution:Universidad de Barcelona
Repository:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/225686
Online Access:https://hdl.handle.net/2445/225686
Access Level:Open access
Keyword:Superfícies algebraiques
Homologia
Algebraic surfaces
Homology
Description
Summary:In this work we study the moduli spaces of instanton bundles on the flag twistor space $F:=F(0,1,2)$. We stratify them in terms of the minimal twist supporting global sections and we introduce the notion of (special) 't Hooft bundle on $F$. In particular we prove that there exist $\mu$-stable 't Hooft bundles for each admissible charge $k$. We completely describe the geometric structure of the moduli space of (special) 't Hooft bundles for arbitrary charge $k$. Along the way to reach these goals, we describe the possible structures of multiple curves supported on some rational curves in $F$ as well as the family of del Pezzo surfaces realized as hyperplane sections of $F$. Finally we investigate the splitting behavior of 't Hooft bundles when restricted to conics.