Donagi–Markman cubics for Hitchin systems of type $$A_2$$, $$B_2$$, $$G_2$$
Abstract We obtain explicit formulae for the Donagi–Markman (Bryant–Griffiths, Yukawa) cubic for Hitchin systems of type $$A_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> , $$B_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> and $$G_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>G</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> . This is achieved by evaluating the quadratic residues in the Balduzzi–Pantev formula, using a previous result of ours. For $$G_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>G</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> we also recover earlier results of Hitchin.
Authors
- Peter Dalakov
- Ugo Bruzzo (ORCID: https://orcid.org/0000-0001-8726-1729)
Institutions
- Scuola Internazionale Superiore di Studi Avanzati (IT)
- American University in Bulgaria (BG)
- Bulgarian Academy of Sciences (BG)
- Institute of Mathematics and Informatics (BG)
- Istituto Nazionale di Fisica Nucleare, Sezione di Trieste (IT)
- Institute for Geometry and Physics
Publication Details
- Journal
- Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas
- Published
- 2025-05-29
- DOI
- https://doi.org/10.1007/s13398-025-01741-0
- Primary Topic
- Algebraic Geometry and Number Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Scuola Internazionale Superiore di Studi Avanzati
- Ministero dell'Università e della Ricerca
- Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni