The associated map of the nonabelian Gauss-Manin connection

• Autorzy: Ting Chen
• Języki publikacji: EN

Abstrakty

EN

The Gauss-Manin connection for nonabelian cohomology spaces is the isomonodromy flow. We write down explicitly the vector fields of the isomonodromy flow and calculate its induced vector fields on the associated graded space of the nonabelian Hogde filtration. The result turns out to be intimately related to the quadratic part of the Hitchin map.

Słowa kluczowe

EN

Gauss-Manin connection; Isomonodromy flow; Hogde filtration; Hitchin map

Kategorie tematyczne

• 14H60: Vector bundles on curves and their moduli
• 14H70: Relationships with integrable systems

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 4
• Strony: 1407-1421

Daty

wydano

2012-08-01

online

2012-05-31

Twórcy

autor

Ting Chen

• University of Pennsylvania

Bibliografia

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• [4] Inaba M., Iwasaki K., Saito M.-H., Moduli of stable parabolic connections, Riemann-Hilbert correspondence and geometry of Painlevé equation of type VI, Part I, Publ. Res. Inst. Math. Sci., 2006, 42(4), 987–1089 http://dx.doi.org/10.2977/prims/1166642194
• [5] Markman E., Spectral curves and integrable systems, Compositio Math., 1994, 93(3), 255–290
• [6] Mumford D., Projective invariants of projective structures and applications, In: Proc. Internat. Congr. Mathematicians, Stockholm, 1962, Inst. Mittag-Leffler, Djursholm, 1963, 526–530
• [7] Simpson C., The Hodge filtration on nonabelian cohomology, In: Algebraic Geometry, Santa Cruz, 1995, Proc. Sympos. Pure Math., 62(2), American Mathematical Society, Providence, 1997, 217–281

Identyfikatory

DOI

10.2478/s11533-011-0110-3