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Qualitative aspects of counting real rational curves on real K3 surfaces

Viatcheslav Kharlamov and Rareş Răsdeaconu

Geometry & Topology 21 (2017) 585–601
Bibliography
1 E Brugallé, G Mikhalkin, Enumeration of curves via floor diagrams, C. R. Math. Acad. Sci. Paris 345 (2007) 329 MR2359091
2 J Bryan, N C Leung, The enumerative geometry of K3 surfaces and modular forms, J. Amer. Math. Soc. 13 (2000) 371 MR1750955
3 X Chen, A simple proof that rational curves on K3 are nodal, Math. Ann. 324 (2002) 71 MR1931759
4 C Ciliberto, A Lopez, R Miranda, Projective degenerations of K3 surfaces, Gaussian maps, and Fano threefolds, Invent. Math. 114 (1993) 641 MR1244915
5 A I Degtyarev, V M Kharlamov, Topological properties of real algebraic varieties : Rokhlin’s way, Uspekhi Mat. Nauk 55 (2000) 129 MR1786731
6 P Di Francesco, C Itzykson, Quantum intersection rings, from: "The moduli space of curves" (editors R Dijkgraaf, C Faber, G van der Geer), Progr. Math. 129, Birkhäuser (1995) 81 MR1363054
7 S Finashin, V Kharlamov, Abundance of real lines on real projective hypersurfaces, Int. Math. Res. Not. 2013 (2013) 3639 MR3090704
8 S Finashin, V Kharlamov, Abundance of 3–planes on real projective hypersurfaces, Arnold Math. J. 1 (2015) 171 MR3370064
9 D B Grünberg, P Moree, Sequences of enumerative geometry: congruences and asymptotics, Experiment. Math. 17 (2008) 409 MR2484425
10 G H Hardy, S Ramanujan, Asymptotic formulae in combinatory analysis, Proc. London Math. Soc. (2) 17 (1918) 75 MR1575586
11 I Itenberg, V Kharlamov, E Shustin, Welschinger invariant and enumeration of real rational curves, Int. Math. Res. Not. 2003 (2003) 2639 MR2012521
12 I Itenberg, V Kharlamov, E Shustin, Logarithmic asymptotics of the genus zero Gromov–Witten invariants of the blown up plane, Geom. Topol. 9 (2005) 483 MR2140988
13 I Itenberg, V Kharlamov, E Shustin, Welschinger invariants of real del Pezzo surfaces of degree 2, Internat. J. Math. 26 (2015) MR3372187
14 V M Kharlamov, Additional congruences for the Euler characteristic of even-dimensional real algebraic varieties, Funkcional. Anal. i Priložen. 9 (1975) 51 MR0401770
15 V Kharlamov, R Răsdeaconu, Counting real rational curves on K3 surfaces, Int. Math. Res. Not. 2015 (2015) 5436 MR3384445
16 G Köhler, Eta products and theta series identities, Springer (2011) MR2766155
17 V S Kulikov, Degenerations of K3 surfaces and Enriques surfaces, Izv. Akad. Nauk SSSR Ser. Mat. 41 (1977) 1008 MR0506296
18 J Lehner, Further congruence properties of the Fourier coefficients of the modular invariant j(τ), Amer. J. Math. 71 (1949) 373 MR0027802
19 V V Nikulin, Integer symmetric bilinear forms and some of their geometric applications, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979) 111, 238 MR525944
20 V V Nikulin, S Saito, Real K3 surfaces with non-symplectic involution and applications, Proc. London Math. Soc. 90 (2005) 591 MR2137825
21 J V Uspensky, Asymptotic formulae for numerical functions which occur in the theory of partitions, Bull. Acad. Sci. URSS (6) 14 (1920) 199
22 O Y Viro, Construction of multicomponent real algebraic surfaces, Dokl. Akad. Nauk SSSR 248 (1979) 279 MR553188
23 J Y Welschinger, Invariants of real rational symplectic 4–manifolds and lower bounds in real enumerative geometry, C. R. Math. Acad. Sci. Paris 336 (2003) 341 MR1976315
24 J Y Welschinger, Optimalité, congruences et calculs d’invariants des variétés symplectiques réelles de dimension quatre, preprint (2007) arXiv:0707.4317
25 S T Yau, E Zaslow, BPS states, string duality, and nodal curves on K3, Nuclear Phys. B 471 (1996) 503 MR1398633