Modular Vector Fields for Lattice Polarized K3 (2404.06662v1)
Abstract: We consider a moduli space of lattice polarized K3 surfaces with the additional information of a frame of the trascendental cohomology with respect to the lattice polarization. This moduli space is proved to be quasi-affine, and the existence of vector fields on it, called modular vector fields, is proved. A purely algebraic version of the algebra of Siegel quasi-modular forms is obtained as the algebra of global regular functions over this moduli space, with a differential structure coming from the modular vector fields. By means of trascendental considerations we are able to obtain a differential algebra of meromorphic Siegel quasi-modular forms from the previous algebra.
- Murad Alim. Algebraic structure of tt* equations for Calabi-Yau sigma models. Communications in Mathematical Physics, 2017.
- Gauss-Manin Lie algebra of mirror elliptic K3 surfaces. Mathematical Research Letters, 2021.
- L. Baily and A. Borel. Compactification of arithmetic quotients of bounded symmetric domains. Annals of Mathematics, 1966.
- P. Bender. Presentation of symplectic group Sp(4,Z) with 2 generatrices and 8 definitive relations. Journal of Algebra 65, no. 2, 1980.
- H. Cartan. Quotients d’un espace analytique par un groupe d’automorphismes. Algebraic Geometry and Topology, 1957.
- Lattice polarized K3 surfaces and Siegel modular forms. Journal of Mathematical Sciences, 2010.
- Period Mappings and Period Domains. Cambridge Studies in Advanced Mathematics 85. Cambridge University Press, 2003.
- Pierre Deligne. Théorie de Hodge III. Publ. Math. I.H.E.S., 1972.
- Humbert surfaces and the moduli of lattice polarized K3 surfaces. String-Math 2014, American Mathematical Society, Proceedings of Symposia in Pure Mathematics 93, 124-155., 2016.
- Tiago Fonseca. Higher Ramanujan equations I: moduli stacks of abelian varieties and higher Ramanujan vector fields. arXiv:1612.05081, 2019.
- TJD Fonseca. Higher ramanujan equations and periods of abelian varieties. Memoirs of the American Mathematical Society, 2020.
- V. Gritsenko and V. Nikulin. Siegel automorphic form corrections of some Lorentzian Kac-Moody Lie algebras. Amer. J. Math. vol. 119, no. 1, 1997.
- H. Grauert and R. Remmert. Coherent Analytic Sheaves. Grundlehren Der Mathematischen Wissenschaften. Springer, 1984.
- Phillip A. Griffiths. Periods of integrals on algebraic manifolds, I. (construction and properties of the modular varieties). American Journal of Mathematics, 1968.
- Daniel Huybrechts. Lectures on K3 Surfaces. 2016.
- J. Igusa. On the ring of modular forms of degree two over ℤℤ\mathbb{Z}blackboard_Z. Amer. J. Math., 1979.
- Qing Liu. Algebraic Geometry and Arithmetic Curves. Oxford University Press, 2002.
- Hossein Movasati. Differential modular forms and some analytic relations between eisenstein series. Ramanujan Journal, 2008.
- Hossein Movasati. On Ramanujan relations between eisenstein series. Manuscripta Mathematica, 2012.
- Hossein Movasati. Quasi-modular forms attached to elliptic curves, I. Annales Mathématiques Blaise Pascal, 2012.
- Hossein Movasati. Quasi-modular forms attached to Hodge structures. Fields Communication Series, 2013.
- Hossein Movasati. Gauss-Manin connection in disguise: Calabi-Yau modular forms. International Press, 2017.
- Hossein Movasati. A Course in Hodge Theory: with Emphasis on Multiple Integrals. International Press of Boston, 2021.
- Hossein Movasati. Modular and Automorphic Forms & beyond., volume 9. World Scientific, 2021.
- J. H. M. Steenbrink. Mixed hodge structure on the vanishing cohomology. Symposium in Mathematics, 1976.
- Jean-Luois Verdier. Stratifications de Whitney et théorème de Bertini-Sard. Inventiones mathematicae, 1976.
- Martin Vogrin. Algebraic Structures on Moduli Spaces of Mirror Geometries. 2020.
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