@article{SIGMA_2019_15_a0,
author = {Florian Beck},
title = {Aspects of {Calabi{\textendash}Yau} {Integrable} and {Hitchin} {Systems}},
journal = {Symmetry, integrability and geometry: methods and applications},
year = {2019},
volume = {15},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a0/}
}
Florian Beck. Aspects of Calabi–Yau Integrable and Hitchin Systems. Symmetry, integrability and geometry: methods and applications, Tome 15 (2019). http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a0/
[1] Anderson L. B., Esole M., Fredrickson L., Schaposnik L. P., “Singular geometry and Higgs bundles in string theory”, SIGMA, 14 (2018), 037, 27 pp., arXiv: 1710.08453 | DOI | MR | Zbl
[2] Anderson L. B., Heckman J. J., Katz S., “T-branes and geometry”, J. High Energy Phys., 2014:5 (2014), 080, 68 pp., arXiv: 1310.1931 | DOI | MR | Zbl
[3] Anderson L. B., Heckman J. J., Katz S., Schaposnik L. P., “T-branes at the limits of geometry”, J. High Energy Phys., 2017:10 (2017), 058, 56 pp., arXiv: 1702.06137 | DOI | MR
[4] Beck F., Hitchin and Calabi–Yau integrable systems, Ph.D. Thesis, Albrecht-Ludwigs Universität Freiburg, 2016 | DOI | Zbl
[5] Beck F., Hitchin and Calabi–Yau integrable systems via variations of Hodge structures, arXiv: 1707.05973
[6] Beck F., “Calabi–Yau orbifolds over Hitchin bases”, J. Geom. Phys., 136 (2019), 14–30, arXiv: 1807.05134 | DOI | MR
[7] Birkenhake C., Lange H., Complex tori, Progress in Mathematics, 177, Birkhäuser Boston, Inc., Boston, MA, 1999 | DOI | MR | Zbl
[8] Birkenhake C., Lange H., Complex abelian varieties, Grundlehren der Mathematischen Wissenschaften, 302, 2nd ed., Springer-Verlag, Berlin, 2004 | DOI | MR | Zbl
[9] Bogomolov F. A., “Kähler manifolds with trivial canonical class”, Izv. Akad. Nauk SSSR Ser. Mat., 38 (1974), 11–21 | MR | Zbl
[10] Brieskorn E., “Singular elements of semi-simple algebraic groups”, Actes du Congrès International des Mathématiciens (Nice, 1970), v. 2, Gauthier-Villars, Paris, 1971, 279–284 | MR
[11] Clemens C. H., Griffiths P. A., “The intermediate Jacobian of the cubic threefold”, Ann. of Math., 95 (1972), 281–356 | DOI | MR | Zbl
[12] Collingwood D. H., McGovern W. M., Nilpotent orbits in semisimple Lie algebras, Van Nostrand Reinhold Mathematics Series, Van Nostrand Reinhold Co., New York, 1993 | MR | Zbl
[13] Dalakov P., “Lectures on Higgs moduli and abelianisation”, J. Geom. Phys., 118 (2017), 94–125, arXiv: 1609.00646 | DOI | MR | Zbl
[14] del Angel P. L., Müller-Stach S., “Picard–Fuchs equations, integrable systems and higher algebraic $K$-theory”, Calabi–Yau Varieties and Mirror Symmetry (Toronto, ON, 2001), Fields Inst. Commun., 38, Amer. Math. Soc., Providence, RI, 2003, 43–55, arXiv: math.AG/0207196 | MR | Zbl
[15] Deligne P., “Théorie de Hodge. II”, Inst. Hautes Études Sci. Publ. Math., 1971, 5–57 | DOI | MR | Zbl
[16] Diaconescu D. E., Dijkgraaf R., Donagi R., Hofman C., Pantev T., “Geometric transitions and integrable systems”, Nuclear Phys. B, 752 (2006), 329–390, arXiv: hep-th/0506196 | DOI | MR | Zbl
[17] Diaconescu D. E., Donagi R., Pantev T., “Intermediate Jacobians and $ADE$ Hitchin systems”, Math. Res. Lett., 14 (2007), 745–756, arXiv: hep-th/0607159 | DOI | MR | Zbl
[18] Donagi R., “Decomposition of spectral covers”, Astérisque, 218, 1993, 145–175 | MR | Zbl
[19] Donagi R., “Spectral covers”, Current Topics in Complex Algebraic Geometry (Berkeley, CA, 1992/93), Math. Sci. Res. Inst. Publ., 28, Cambridge University Press, Cambridge, 1995, 65–86, arXiv: alg-geom/9505009 | MR | Zbl
[20] Donagi R., “Seiberg–Witten integrable systems”, Algebraic Geometry (Santa Cruz, 1995), Proc. Sympos. Pure Math., 62, Amer. Math. Soc., Providence, RI, 1997, 3–43, arXiv: alg-geom/9705010 | DOI | MR | Zbl
[21] Donagi R., Gaitsgory D., “The gerbe of Higgs bundles”, Transform. Groups, 7 (2002), 109–153, arXiv: math.AG/0005132 | DOI | MR | Zbl
[22] Donagi R., Markman E., “Cubics, integrable systems, and Calabi–Yau threefolds”, Proceedings of the Hirzebruch 65 Conference on Algebraic Geometry (Ramat Gan, 1993), Israel Math. Conf. Proc., 9, Bar-Ilan University, Ramat Gan, 1996, 199–221, arXiv: alg-geom/9408004 | MR | Zbl
[23] Donagi R., Markman E., “Spectral covers, algebraically completely integrable, Hamiltonian systems, and moduli of bundles”, Integrable Systems and Quantum Groups (Montecatini Terme, 1993), Lecture Notes in Math., 1620, Springer, Berlin, 1996, 1–119, arXiv: alg-geom/9507017 | DOI | MR | Zbl
[24] Donagi R., Pantev T., “Langlands duality for Hitchin systems”, Invent. Math., 189 (2012), 653–735, arXiv: math.AG/0604617 | DOI | MR | Zbl
[25] Du Val P., Homographies, quaternions and rotations, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964 | MR | Zbl
[26] Esnault H., Viehweg E., “Deligne–Beĭlinson cohomology”, Beĭlinson's Conjectures on Special Values of $L$-Functions, Perspect. Math., 4, Academic Press, Boston, MA, 1988, 43–91 | MR
[27] Faltings G., “Stable $G$-bundles and projective connections”, J. Algebraic Geom., 2 (1993), 507–568 | MR | Zbl
[28] Griffiths P. A., “Periods of integrals on algebraic manifolds. I. Construction and properties of the modular varieties”, Amer. J. Math., 90 (1968), 568–626 | DOI | MR | Zbl
[29] Hausel T., Thaddeus M., “Mirror symmetry, Langlands duality, and the Hitchin system”, Invent. Math., 153 (2003), 197–229, arXiv: math.AG/0205236 | DOI | MR | Zbl
[30] Hitchin N., “Stable bundles and integrable systems”, Duke Math. J., 54 (1987), 91–114 | DOI | MR | Zbl
[31] Hitchin N. J., “The self-duality equations on a Riemann surface”, Proc. London Math. Soc., 55 (1987), 59–126 | DOI | MR | Zbl
[32] Humphreys J. E., Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, 9, 2nd ed., Springer-Verlag, New York–Berlin, 1978 | DOI | MR | Zbl
[33] Kapustin A., Witten E., “Electric-magnetic duality and the geometric Langlands program”, Commun. Number Theory Phys., 1 (2007), 1–236, arXiv: hep-th/0604151 | DOI | MR | Zbl
[34] Kashiwara M., Schapira P., Sheaves on manifolds, Grundlehren der Mathematischen Wissenschaften, 292, Springer-Verlag, Berlin, 1990 | DOI | MR | Zbl
[35] Kostant B., “Lie group representations on polynomial rings”, Amer. J. Math., 85 (1963), 327–404 | DOI | MR | Zbl
[36] McKay J., “Graphs, singularities, and finite groups”, The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979), Proc. Sympos. Pure Math., 37, Amer. Math. Soc., Providence, R.I., 1980, 183–186 | DOI | MR
[37] Saito M., “Mixed Hodge modules”, Publ. Res. Inst. Math. Sci., 26 (1990), 221–333 | DOI | MR | Zbl
[38] Scognamillo R., “An elementary approach to the abelianization of the Hitchin system for arbitrary reductive groups”, Compositio Math., 110 (1998), 17–37, arXiv: alg-geom/9412020 | DOI | MR | Zbl
[39] Slodowy P., Simple singularities and simple algebraic groups, Lecture Notes in Math., 815, Springer, Berlin, 1980 | DOI | MR | Zbl
[40] Szendrői B., “Artin group actions on derived categories of threefolds”, J. Reine Angew. Math., 572 (2004), 139–166, arXiv: math.AG/0210121 | DOI | MR | Zbl
[41] Tian G., “Smoothness of the universal deformation space of compact Calabi–Yau manifolds and its Petersson–Weil metric”, Mathematical Aspects of String Theory (San Diego, Calif., 1986), Adv. Ser. Math. Phys., 1, World Sci. Publishing, Singapore, 1987, 629–646 | DOI | MR
[42] Todorov A. N., “The Weil–Petersson geometry of the moduli space of ${\rm SU}(n\geq 3)$ (Calabi–Yau) manifolds. I”, Comm. Math. Phys., 126 (1989), 325–346 | DOI | MR | Zbl