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We construct non-geometric compactifications by using the F-theory dual of the heterotic string compactified on a two-torus, together with a close connection between Siegel modular forms of genus two and the equations of certain K3 surfaces.
Ann. of Math. (2) 71
Satake, I.: On representations and compactifications of symmetric Riemannian spaces · 1960
Earlier work this paper cites.
Amer. J. Math. 84
Igusa, J.: On Siegel modular forms of genus two · 1962
Earlier work this paper cites.
Ann. of Math. (2) 77
Kodaira, K.: On compact analytic surfaces. II, III · 1963
Earlier work this paper cites.
Inst. Hautes Études Sci. Publ. Math. 21
Néron, A.: Modèles minimaux des variétés abéliennes sur les corps locaux et globaux · 1964
Earlier work this paper cites.
Ann. of Math. (2) 84
Baily Jr., W.L., Borel, A.: Compactification of arithmetic quotients of bounded symmetric domains · 1966
Earlier work this paper cites.
Amer. J. Math. 89
Igusa, J.: Modular forms and projective invariants · 1967
Earlier work this paper cites.
Manuscripta Math. 9
Namikawa, Y., Ueno, K.: The complete classification of fibres in pencils of curves of genus two · 1973
Earlier work this paper cites.
In: Modular functions of one variable, IV (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), Lecture Notes in Math. , vol. 476, pp. 53–73. Springer, Berlin (1975)
Deligne, P.: Courbes elliptiques: formulaire (d’après J. Tate) · 1975
Earlier work this paper cites.
Amer. J. Math. 101
Igusa, J.i.: On the ring of modular forms of degree two over 𝐙 {\bf Z} · 1979
Earlier work this paper cites.
Izv. Akad. Nauk SSSR Ser. Mat. 43
Nikulin, V.V.: Integral symmetric bilinear forms and some of their applications · 1980
Earlier work this paper cites.
Springer-Verlag, Berlin (1983)
Freitag, E.: Siegelsche Modulfunktionen, Grundlehren der Mathematischen Wissenschaften , vol. 254 · 1983
Earlier work this paper cites.
Math. Ann. 275
Borcea, C.: Diffeomorphisms of a K 3 K3 surface · 1986
Earlier work this paper cites.
In: Algebraic and topological theories (Kinosaki, 1984), pp. 616–621. Kinokuniya, Tokyo (1986)
Matumoto, T.: On diffeomorphisms of a K 3 K3 surface · 1986
Earlier work this paper cites.
Phys. Lett. B 169
Narain, K.S.: New heterotic string theories in uncompactified dimensions < 10 {}<10 · 1986
Earlier work this paper cites.
Nucl. Phys. B 279
Narain, K.S., Sarmadi, M.H., Witten, E.: A note on toroidal compactification of heterotic string theory · 1987
Earlier work this paper cites.
Topology 29
Donaldson, S.K.: Polynomial invariants for smooth four-manifolds · 1990
Earlier work this paper cites.
In: Effective methods in algebraic geometry (Castiglioncello, 1990), Progr. Math. , vol. 94, pp. 313–334. Birkhäuser Boston (1991)
Mestre, J.F.: Construction de courbes de genre 2 2 à partir de leurs modules · 1991
Cited alongside, same era.
Phys. Lett. B 360
Schwarz, J.H.: An SL(2, ℤ \mathbb{Z} ) multiplet of type IIB superstrings · 1995
Cited alongside, same era.
Nucl. Phys. Proc. Suppl. 46
Aspinwall, P.S.: Some relationships between dualities in string theory · 1996
Cited alongside, same era.
Phys. Lett. B 387
Aspinwall, P.S., Gross, M.: The SO ( 32 ) {\rm SO}(32) heterotic string on a K 3 K3 surface · 1996
Cited alongside, same era.
Nuclear Phys. B 481
Bershadsky, M., Intriligator, K., Kachru, S., Morrison, D.R., Sadov, V., Vafa, C.: Geometric singularities and enhanced gauge symmetries · 1996
Cited alongside, same era.
J. Math. Sci. 81
Dolgachev, I.V.: Mirror symmetry for lattice polarized K 3 K3 surfaces · 1996
Cited alongside, same era.
Commun. Math. Phys. 216
Nahm, W., Wendland, K.: A hiker’s guide to K3: Aspects of N = (4,4) superconformal field theory with central charge c = 6 · 2001
Later among the works it cites.
In: Strings, 2001 (Mumbai), Clay Math. Proc. , vol. 1, pp. 139–152. Amer. Math. Soc., Providence, RI (2002)
Douglas, M.R.: D-branes and 𝒩 = 1 \mathcal{N}=1 supersymmetry · 2002
Later among the works it cites.
Comm. Math. Phys. 241
Hosono, S., Lian, B.H., Oguiso, K., Yau, S.T.: c = 2 c=2 rational toroidal conformal field theories via the Gauss product · 2003
Later among the works it cites.
Michigan Math. J. 55
Clingher, A., Doran, C.F.: Modular invariants for lattice polarized K 3 K3 surfaces · 2007
Later among the works it cites.
Invent. Math. 169
Gritsenko, V.A., Hulek, K., Sankaran, G.K.: The Kodaira dimension of the moduli of K 3 K3 surfaces · 2007
Later among the works it cites.
Int. Math. Res. Not. 2008
Kumar, A.: K 3 K3 surfaces associated with curves of genus two · 2008
Later among the works it cites.
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Mat. Sb. 187
Gritsenko, V.A., Nikulin, V.V.: Igusa modular forms and “the simplest” Lorentzian Kac-Moody algebras · 1996
Cited alongside, same era.
Nuclear Phys. B 476
Morrison, D.R., Vafa, C.: Compactifications of F-theory on Calabi–Yau threefolds, II · 1996
Cited alongside, same era.
Nucl. Phys. B 469
Vafa, C.: Evidence for F-theory · 1996
Cited alongside, same era.
Nucl. Phys. B 496
Aspinwall, P.S.: Point-like instantons and the Spin(32)/ ℤ 2 \mathbb{Z}_{2} heterotic string · 1997
Cited alongside, same era.
In: B. Greene, S.T. Yau (eds.) Mirror Symmetry II, pp. 703–716. International Press, Cambridge (1997)
Aspinwall, P.S., Morrison, D.R.: String theory on K3 surfaces · 1997
Cited alongside, same era.
Commun. Math. Phys. 187
Friedman, R., Morgan, J., Witten, E.: Vector bundles and F theory · 1997
Cited alongside, same era.
Adv. Theor. Math. Phys. 14
McOrist, J., Morrison, D.R., Sethi, S.: Geometries, non-geometries, and fluxes · 2010
Later among the works it cites.
Int. Math. Res. Not. IMRN 2011
Clingher, A., Doran, C.F.: Note on a geometric isogeny of K3 surfaces · 2011
Later among the works it cites.
Adv. Math. 231
Clingher, A., Doran, C.F.: Lattice polarized K3 surfaces and Siegel modular forms · 2012
Later among the works it cites.
Class. Quant. Grav. 30
Aldazabal, G., Marques, D., Nunez, C.: Double field theory: A pedagogical review · 2013
Later among the works it cites.
JHEP 1310
Braun, A.P., Fucito, F., Morales, J.F.: U-folds as K3 fibrations · 2013
Later among the works it cites.
Fortsch. Phys. 61
Hohm, O., Lüst, D., Zwiebach, B.: The spacetime of double field theory: Review, remarks, and outlook · 2013
Later among the works it cites.
JHEP 1301
Martucci, L., Morales, J.F., Pacifici, D.R.: Branes, U-folds and hyperelliptic fibrations · 2013
Later among the works it cites.
Trans. Moscow Math. Soc. 2013
Vinberg, E.B.: On the algebra of Siegel modular forms of genus 2 · 2013
Later among the works it cites.
Phys. Rept. 566
Berman, D.S., Thompson, D.C.: Duality symmetric string and M-theory · 2014
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