Normal functions, Picard--Fuchs equations, and elliptic fibrations on K3 surfaces

References

[1] Asakura M., On dlog image of K2 of elliptic surface minus singular fibers, preprint 2008, http://arxiv.org/abs/math/0511190. Search in Google Scholar

[2] Beilinson A., Higher regulators of modular curves, Applications of algebraic K-theory to algebraic geometry and number theory (Boulder 1983), Comtemp. Math. 55, American Mathematical Society, Providence (1986), 1–34. 10.1090/conm/055.1/862627Search in Google Scholar

[3] Bloch S., Algebraic cycles and values of L-functions, J. reine angew. Math. 350 (1984), 94–108. 10.1215/S0012-7094-85-05219-6Search in Google Scholar

[4] Bloch S., Algebraic cycles and higher K-theory, Adv. Math. 61 (1986), 267–304. 10.1016/0001-8708(86)90081-2Search in Google Scholar

[5] Chen X. and Lewis J. D., The Hodge-𝒟-conjecture for K⁢3 and Abelian surfaces, J. Algebraic Geom. 14 (2005), no. 2, 213–240. 10.1090/S1056-3911-04-00390-XSearch in Google Scholar

[6] Chen X. and Lewis J. D., Real regulators on self-products of K3 surfaces, J. Algebraic Geom. 20 (2011), no. 1, 101–125. 10.1090/S1056-3911-09-00525-6Search in Google Scholar

[7] Clingher A. and Doran C. F., Modular invariants for lattice polarized K⁢3 surfaces, Mich. Math. J. 55 (2007), no. 2, 355–393. 10.1307/mmj/1187646999Search in Google Scholar

[8] Clingher A. and Doran C. F., On K⁢3 surfaces with large complex structure, Adv. Math. 215 (2007), 504–539. 10.1016/j.aim.2007.04.014Search in Google Scholar

[9] Clingher A. and Doran C. F., Note on a geometric isogeny of K3 surfaces, Int. Math. Res. Not. IMRN (2010), 10.1093/imrn/rnq230. 10.1093/imrn/rnq230Search in Google Scholar

[10] Clingher A. and Doran C. F., Lattice polarized K3 surfaces and Siegel modular forms, Adv. Math. 231 (2012), 172–212. 10.1016/j.aim.2012.05.001Search in Google Scholar

[11] Clingher A., Doran C., Lewis J. M. and Whitcher U., Normal forms, K3 surface moduli, and modular parametrizations, Groups and symmetries: From Neolithic Scots to John McKay, CRM Proc. Lect. Notes 47, (2009), 81–98. 10.1090/crmp/047/06Search in Google Scholar

[12] del Angel P. L. and Müller-Stach S. J., The transcendental part of the regulator map for K1 on a mirror family of K⁢3-surfaces, Duke Math. J. 112 (2002), no. 3, 581–598. 10.1215/S0012-9074-02-11236-8Search in Google Scholar

[13] Deligne P., Théorème de Lefschetz et critères de dégénérescence de suites spectrales, Inst. Hautes Études Sci. Publ. Math. 35 (1968), 259–278. 10.1007/BF02698925Search in Google Scholar

[14] Dolgachev I. V., Mirror symmetry for lattice polarized K3 surfaces, J. Math. Sci. 81 (1996), no. 3, 2599–2630. 10.1007/BF02362332Search in Google Scholar

[15] Doran C. F., Picard–Fuchs uniformization and modularity of the mirror map, Comm. Math. Phys. 212 (2000), no. 3, 625–647. 10.1007/s002200000228Search in Google Scholar

[16] Doran C. F., Picard–Fuchs uniformization: Modularity of the mirror map and mirror moonshine, The arithmetic and geometry of algebraic cycles (Banff 1998), CRM Proc. Lect. Notes 24, American Mathematical Society, Providence (2000), 257–281. 10.1090/crmp/024/13Search in Google Scholar

[17] Gordon B. and Lewis J. D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543–567. Search in Google Scholar

[18] Griffiths P. A., A theorem concerning the differential equations satisfied by normal functions associated to algebraic cycles, Amer. J. Math. 101 (1979), no. 1, 94–131. 10.2307/2373941Search in Google Scholar

[19] Harris B., Homological versus algebraic equivalence in a Jacobian, Proc. Nat. Acad. Sci. U.S.A. 80 (1983), no. 4 i, 1157–1158. 10.1073/pnas.80.4.1157Search in Google Scholar PubMed PubMed Central

[20] Kerr M., K1ind of elliptically fibered K⁢3 surfaces: A tale of two cycles, Arithmetic and geometry of K⁢3 surfaces and Calabi–Yau threefolds, Fields Inst. Commun. 67, Springer, New York (2013), 387–409. 10.1007/978-1-4614-6403-7_13Search in Google Scholar

[21] Kerr M. and Lewis J. D., The Abel–Jacobi map for higher Chow groups, II, Invent. Math. 170 (2007), no. 2, 355–420. 10.1007/s00222-007-0066-xSearch in Google Scholar

[22] Kerr M., Lewis J. D. and Müller-Stach S., The Abel–Jacobi map for higher Chow groups, Compositio Math. 142 (2006), 374–396. 10.1112/S0010437X05001867Search in Google Scholar

[23] Lewis J. D., A note on indecomposable motivic cohomology classes, J. reine angew. Math. 485 (1997), 161–172. 10.1515/crll.1997.485.161Search in Google Scholar

[24] Morrison D. and Walcher J., D-branes and normal functions, Adv. Theor. Math. Phys. 13 (2009), 553–598. 10.4310/ATMP.2009.v13.n2.a5Search in Google Scholar

[25] Müller-Stach S., Constructing indecomposable motivic cohomology classes on algebraic surfaces, J. Algebraic Geom. 6 (1997), 513–543. Search in Google Scholar

[26] Novoseltsev A., Calabi–Yau hypersurfaces and complete intersections in toric varieties, Ph.D. thesis, University of Alberta, 2011. Search in Google Scholar

[27] Turkmen I. U., Regulator indecomposable cycles on a product of elliptic curves, Canad. Math. Bull. 56 (2013), no. 3, 640–646. 10.4153/CMB-2012-017-xSearch in Google Scholar

[28] Whitcher U., Polarized families of K3 hypersurfaces, Ph.D. thesis, University of Washington, 2009. Search in Google Scholar

[29] Zigmond R., Triangle configurations and Beilinson’s conjecture for K1(2) of the product of a curve with itself, Ph.D. thesis, Durham University, 2010. Search in Google Scholar