Abstract
We consider minimal semisimple adjoint orbits as Landau–Ginzburg models and prove that they satisfy the conjecture of Katzarkov–Kontsevich–Pantev about new Hodge theoretical invariants.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ballico, E., Barmeier, S., Gasparim, E., Grama, L., San Martin, L..A..B.: A Lie theoretical construction of a Landau-Ginzburg model without projective mirrors. Manuscripta Math. 158(1–2), 85–101 (2019)
Ballico, E., Callander, B., Gasparim, E.: Compactifications of adjoint orbits and their Hodge diamonds. J. Algebra Appl. 17(6), 1850099 (2018)
Ballico, E., Gasparim, E., Grama, L., San Martin, L..A..B.: Some Landau–Ginzburg models viewed as rational maps. Indag. Math. (N.S.) 28(3), 615–628 (2017)
Cheltsov, I., Przyjalkowski, V.: Katzarkov–Kontsevich–Pantev Conjecture for Fano threefolds (2018). arxiv:1809.09218
Durfee, A..H.: Algebraic varieties which are a disjoint union of subvarieties. In: McCrory, C. (ed.) Geometry and Topology (Athens, Ga., 1985). Lecture Notes in Pure and Applied Mathematics, vol. 105, pp. 99–102. Dekker, New York (1987)
Gasparim, E., Grama, L., San Martin, L.A.B.: Symplectic Lefschetz fibrations on adjoint orbits. Forum Math. 28(5), 967–979 (2016)
Gasparim, E., Grama, L., San Martin, L.A.B.: Adjoint orbits of semi-simple Lie groups and Lagrangian submanifolds. Proc. Edinburgh Math. Soc. 60(2), 361–385 (2017)
Griffiths, P., Harris, J.: Principles of Algebraic Geometry. Reprint of the 1978 original. Wiley Classics Library. Wiley, New York (1994)
Gross, M., Katzarkov, L., Ruddat, H.: Towards mirror symmetry for varieties of general type. Adv. Math. 308, 208–275 (2017)
Harder, A.: Hodge numbers of Landau-Ginzburg models. Adv. Math. 378, 107436 (2021)
Howe, S.: Introduction to Mixed Hodge Theory and Hodge II. Lecture Notes, University of Chicago (2014). https://www.math.utah.edu/~howe/notes/mixed-hodge.pdf
Katz, N.M.: Nilpotent connections and the monodromy theorem: applications of a result of Turrittin. Inst. Hautes Études Sci. Publ. Math. 39, 175–232 (1970)
Katzarkov, L., Kontsevich, M., Pantev, T.: Bogomolov–Tian–Todorov theorems for Landau–Ginzburg models. J. Differ. Geom. 105(1), 55–117 (2017)
Lunts, V., Przyjalkowski, V.: Landau–Ginzburg Hodge numbers for mirrors of del Pezzo surfaces. Adv. Math. 329, 189–216 (2018)
Shamoto, Y.: Hodge–Tate conditions for Landau–Ginzburg models. Publ. Res. Inst. Math. Sci. 54(3), 469–515 (2018)
Acknowledgements
We thank the referee for many useful suggestions.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Ballico was partially supported by MIUR and GNSAGA of INdAM (Italy). Gasparim was partially supported by the Vicerrectoría de Investigación y Desarrollo Tecnológico de la Universidad Católica del Norte (Chile). Rubilar acknowledges support from Beca Doctorado Nacional – Folio 21170589. Gasparim and Rubilar were partially supported by Network NT8 of the Office of External Activities of ICTP (Italy).
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Ballico, E., Gasparim, E., Rubilar, F. et al. The Katzarkov–Kontsevich–Pantev conjecture for minimal adjoint orbits. European Journal of Mathematics 9, 57 (2023). https://doi.org/10.1007/s40879-023-00652-x
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40879-023-00652-x