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Original Articles

Quantum Periods for Certain Four-Dimensional Fano Manifolds

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References

  • [Akhtar et al. 16] M. Akhtar, T. Coates, A. Corti, L. Heuberger, A. Kasprzyk, A. Oneto, A. Petracci, T. Prince, and K. Tveiten. “Mirror Symmetry and the Classification of Orbifold del Pezzo Surfaces,” Proc. Amer. Math. Soc. 144:2 (2016), 513–527.
  • [Batyrev 99] V. V. Batyrev. “On the Classification of Toric Fano 4-Folds,” J. Math. Sci. (New York) 94:1 (1999), 1021–1050.
  • [Batyrev et al. 98] V. V. Batyrev, I. Ciocan-Fontanine, B. Kim, and D. van Straten. “Conifold Transitions and Mirror Symmetry for Calabi-Yau Complete Intersections in Grassmannians,” Nucl. Phys. B 514:3 (1998), 640–666.
  • [Batyrev et al. 00] V. V. Batyrev, I. Ciocan-Fontanine, B. Kim, and D. van Straten. “Mirror Symmetry and Toric Degenerations of Partial Flag Manifolds,” Acta Math. 184:1 (2000), 1–39.
  • [Bosma et al. 97] W. Bosma, J. Cannon, and C. Playoust. “The Magma Algebra System. I. The User Language,” J. Symb. Comput. 24:3–4 (1997), 235–265.
  • [Brown and Kasprzyk] G. Brown and A. Kasprzyk. “The Graded Ring Database,” Available online http://www.grdb.co.uk/.
  • [Cavey and Prince 17] D. Cavey and T. Prince. “Del Pezzo Surfaces with a Single 1k(1,1) Singularity,” arXiv:1707.09213 [math.AG], 2017.
  • [CC0] CC0, “Creative Commons CC0 License,” Available online https://creativecommons.org/publicdomain/zero/1.0/ and https://creativecommons.org/publicdomain/zero/1.0/legalcode.
  • [Ciocan-Fontanine et al. 08] I. Ciocan-Fontanine, B. Kim, and C. Sabbah. “The Abelian/nonabelian Correspondence and Frobenius Manifolds,” Invent. Math. 171:2 (2008), 301–343.
  • [Coates 14] T. Coates. “The Quantum Lefschetz Principle for Vector Bundles as a Map Between Givental Cones,” arXiv:1405.2893 [math.AG], 2014.
  • [Coates et al. 12] T. Coates, A. Corti, S. Galkin, V. Golyshev, and A. Kasprzyk. “Mirror Symmetry and Fano Manifolds.” European Congress of Mathematics, Kraków, July 2–7, 2012, 2014, pp. 285–300.
  • [Coates et al. 16] T. Coates, A. Corti, S. Galkin, and A. Kasprzyk. “Quantum Periods for 3-dimensional Fano Manifolds,” Geom. Topol. 20:1 (2016), 103–256.
  • [Coates et al. 14] T. Coates, A. Corti, H. Iritani, and H.-H. Tseng. “Some Applications of the Mirror theorem for Toric Stacks,” arXiv:1401:2611 [math.AG], 2014.
  • [Coates and Givental 07] T. Coates and A. Givental. “Quantum Riemann-Roch, Lefschetz and Serre,” Ann. Math. (2) 165:1 (2007), 15–53.
  • [Corti and Heuberger 17] A. Corti and L. Heuberger. “Del Pezzo Surfaces with 13(1,1) Points,” Manuscr. Math. 153:1–2 (2017), 71–118.
  • [Fujita 80] T. Fujita. “On the Structure of Polarized Manifolds with Total Deficiency One. I,” J. Math. Soc. Japan 32:4 (1980), 709–725.
  • [Fujita 81] T. Fujita. “On the Structure of Polarized Manifolds with Total Deficiency One. II,” J. Math. Soc. Japan 33:3 (1981), 415–434.
  • [Fujita 84] T. Fujita. “On the Structure of Polarized Manifolds with Total Deficiency One. III, J. Math. Soc. Japan 36:1 (1984), 75–89.
  • [Fujita 90] T. Fujita, Classification Theories of Polarized Varieties. In London Mathematical Society Lecture Note Series, vol. 155. Cambridge: Cambridge University Press, 1990.
  • [Givental 96] A. Givental. “A Mirror Theorem for Toric Complete Intersections.” In Topological Field Theory, Primitive Forms and Related Topics (Kyoto, 1996), pp. 141–175, Progr. Math., vol. 160. Boston, MA: Birkhäuser, 1998.
  • [Hartshorne 77] R. Hartshorne. “Algebraic Geometry.” In Graduate Texts in Mathematics, vol. 52. New York-Heidelberg: Springer-Verlag, 1977.
  • [Iskovskih 77] V. A. Iskovskih. “Fano Threefolds. I,” Izv. Akad. Nauk SSSR Ser. Mat. 41:3 (1977), 516–562, 717.
  • [Iskovskih 78] V. A. Iskovskih. “Fano Threefolds. II,” Izv. Akad. Nauk SSSR Ser. Mat. 42:3 (1978), 506–549.
  • [Iskovskih 79] V. A. Iskovskih. “Anticanonical Models of Three-dimensional Algebraic Varieties.” In Current Problems in Mathematics, vol. 12 (Russian), pp. 59–157, Moscow: VINITI, 1979; 239 (loose errata).
  • [Iskovskikh and Prokhorov 99] V. A. Iskovskikh and Yu. G. Prokhorov. “Fano Varieties, Algebraic Geometry, V.” In Encyclopaedia Math. Sci., vol. 47, pp. 1–247, Berlin: Springer, 1999.
  • [Kasprzyk et al. 17] A. Kasprzyk, B. Nill, and T. Prince. “Minimality and Mutation-Equivalence of Polygons,” Forum Math. Sigma 5:e18 (2017), 48.
  • [Kasprzyk and Tveiten ] A. Kasprzyk and K. Tveiten. “Maximally Mutable Laurent Polynomials,” in preparation.
  • [Kedlaya 10] K. S. Kedlaya. “p-adic Differential Equations.” In Cambridge Studies in Advanced Mathematics, vol. 125. Cambridge: Cambridge University Press, 2010.
  • [Kobayashi and Ochiai 73] S. Kobayashi and T. Ochiai. “Characterizations of Complex Projective Spaces and Hyperquadrics,” J. Math. Kyoto Univ. 13 (1973), 31–47.
  • [Kollár 81] Y. Kollár. “Higher-dimensional Fano Varieties of Large Index,” Vestnik Moskov. Univ. Ser. I Mat. Mekh. no. 3 (1981), 31–34, 80–81.
  • [Lairez 16] P. Lairez. “Computing Periods of Rational Integrals, Math. Comp. 85:300 (2016), 1719–1752.
  • [Mori and Mukai 82] S. Mori and S. Mukai. “Classification of Fano 3-folds with B2 ⩾ 2,” Manusc. Math. 36:2 (1981/82), 147–162.
  • [Mori and Mukai 83] S. Mori and S. Mukai. “On Fano 3-Folds with B2 ⩾ 2.” In Algebraic Varieties and Analytic Varieties (Tokyo, 1981), pp. 101–129, Adv. Stud. Pure Math., vol. 1. Amsterdam: North-Holland, 1983.
  • [Mori and Mukai 86] S. Mori and S. Mukai. “Classification of Fano 3-Folds with B2 ⩾ 2. I.” Algebraic and Topological Theories (Kinosaki, 1984), pp. 496–545, Tokyo: Kinokuniya, 1986.
  • [Mori and Mukai 03] S. Mori and S. Mukai. “Erratum: “Classification of Fano 3-folds with B2 ⩾ 2 [Manuscripta Math. 36 (1981/82), no. 2, 147–162],” Manusc. Math. 110:3 (2003), 407.
  • [Mori and Mukai 04] S. Mori and S. Mukai. “Extremal Rays and Fano 3-Folds.” The Fano Conference, Univ. Torino, Turin, 2004, pp. 37–50.
  • [Mukai 88] S. Mukai. “Curves, K3 Surfaces and Fano 3-folds of Genus ⩽ 10.” In Algebraic Geometry and Commutative Algebra, vol. I, pp. 357–377, Tokyo: Kinokuniya, 1988.
  • [Mukai 89] S. Mukai. “Biregular Classification of Fano 3-folds and Fano Manifolds of Coindex 3,” Proc. Nat. Acad. Sci. U.S.A. 86:9 (1989), 3000–3002.
  • [Øbro 07] M. Øbro. “An Algorithm for the Classification of Smooth Fano Polytopes,” arXiv:0704.0049 [math.CO], 2007.
  • [Oneto and Petracci ] A. Oneto and A. Petracci. “On the Quantum Periods of del Pezzo Surfaces with 13(1,1) Singularities,” to appear in Adv. Geom. arXiv:1507.08589 [math.AG].
  • [Sato 00] H. Sato. “Toward the Classification of Higher-dimensional Toric Fano Varieties,” Tohoku Math. J. (2) 52:3 (2000), 383–413.
  • [Serpico 80] M. E. Serpico. “Fano Varieties of Dimensions n ⩾ 4 and of Index r ⩾ n − 1,” Rend. Sem. Mat. Univ. Padova 62 (1980), 295–308.
  • [Shokurov 85] V. V. Shokurov. “A Nonvanishing Theorem,” Izv. Akad. Nauk SSSR Ser. Mat. 49:3 (1985), 635–651.
  • [Steel 10] A. K. Steel. “Computing with Algebraically Closed Fields,” J. Symb. Comput. 45:3 (2010), 342–372.
  • [Strangeway 14] A. Strangeway. “Quantum Reconstruction for Fano Bundles,” PhD diss., Imperial College London, 2014.
  • [Strangeway 15] A. Strangeway. “Quantum Reconstruction for Fano Bundles on Projective Space,” Nagoya Math. J. 218 (2015), 1–28.
  • [Szurek and Wiśniewski 90] M. Szurek and J. A. Wiśniewski. “Fano Bundles Over P3 and Q3,” Pac. J. Math. 141:1 (1990), 197–208.
  • [Wilson 87] P. M. H. Wilson. “Fano Fourfolds of Index Greater than One,” J. Reine Angew. Math. 379 (1987), 172–181.
  • [Wiśniewski 90] J. Wiśniewski. “Fano 4-folds of Index 2 with b2 ⩾ 2. A Contribution to Mukai Classification,” Bull. Polish Acad. Sci. Math. 38:1–12 (1990), 173–184.