Nous construisons un modèle de Landau-Ginzburg pour les intersections complètes numériquement effectives dans les variétés toriques lisses. Il s'agit de compactifications partielles de familles de polynômes de Laurent. Nous démontrons un théorème de symétrie miroir qui exprime le
We construct Landau-Ginzburg models for numerically effective complete intersections in toric manifolds as partial compactifications of families of Laurent polynomials. We show a mirror statement saying that the quantum
DOI : 10.24033/asens.2330
Keywords: Gauß-Manin system, hypergeometric
Mot clés : Systèmes de Gauß-Manin,
@article{ASENS_2017__50_3_665_0, author = {Reichelt, Thomas and Sevenheck, Christian}, title = {Non-affine {Landau-Ginzburg} models and intersection cohomology}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {665--753}, publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es}, volume = {Ser. 4, 50}, number = {3}, year = {2017}, doi = {10.24033/asens.2330}, mrnumber = {3665553}, language = {en}, url = {https://www.numdam.org/articles/10.24033/asens.2330/} }
TY - JOUR AU - Reichelt, Thomas AU - Sevenheck, Christian TI - Non-affine Landau-Ginzburg models and intersection cohomology JO - Annales scientifiques de l'École Normale Supérieure PY - 2017 SP - 665 EP - 753 VL - 50 IS - 3 PB - Société Mathématique de France. Tous droits réservés UR - https://www.numdam.org/articles/10.24033/asens.2330/ DO - 10.24033/asens.2330 LA - en ID - ASENS_2017__50_3_665_0 ER -
%0 Journal Article %A Reichelt, Thomas %A Sevenheck, Christian %T Non-affine Landau-Ginzburg models and intersection cohomology %J Annales scientifiques de l'École Normale Supérieure %D 2017 %P 665-753 %V 50 %N 3 %I Société Mathématique de France. Tous droits réservés %U https://www.numdam.org/articles/10.24033/asens.2330/ %R 10.24033/asens.2330 %G en %F ASENS_2017__50_3_665_0
Reichelt, Thomas; Sevenheck, Christian. Non-affine Landau-Ginzburg models and intersection cohomology. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 50 (2017) no. 3, pp. 665-753. doi : 10.24033/asens.2330. https://www.numdam.org/articles/10.24033/asens.2330/
Hypergeometric functions and rings generated by monomials, Duke Math. J., Volume 73 (1994), pp. 269-290 (ISSN: 0012-7094) | DOI | MR | Zbl
Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties, J. Algebraic Geom., Volume 3 (1994), pp. 493-535 (ISSN: 1056-3911) | MR | Zbl
Mirror duality and string-theoretic Hodge numbers, Invent. math., Volume 126 (1996), pp. 183-203 (ISSN: 0020-9910) | DOI | MR | Zbl
, Higher-dimensional complex varieties (Trento, 1994), de Gruyter, Berlin, 1996, pp. 39-65 | MR | Zbl
, Cambridge Studies in Advanced Math., 39, Cambridge Univ. Press, Cambridge, 1993, 403 pages (ISBN: 0-521-41068-1) | MR | Zbl
Transformations canoniques, dualité projective, théorie de Lefschetz, transformations de Fourier et sommes trigonométriques, Astérisque, Volume 140-141 (1986), p. 3-134, 251 (ISSN: 0303-1179) | Numdam | MR | Zbl
Quantum Riemann-Roch, Lefschetz and Serre, Ann. of Math., Volume 165 (2007), pp. 15-53 (ISSN: 0003-486X) | DOI | MR | Zbl
, Mathematical Surveys and Monographs, 68, Amer. Math. Soc., Providence, RI, 1999, 469 pages (ISBN: 0-8218-1059-6) | DOI | MR | Zbl
, Graduate Studies in Math., 124, Amer. Math. Soc., Providence, RI, 2011, 841 pages (ISBN: 978-0-8218-4819-7) | DOI | MR | Zbl
Topological–anti-topological fusion, Nuclear Phys. B, Volume 367 (1991), pp. 359-461 (ISSN: 0550-3213) | DOI | MR | Zbl
On classification of
Radon and Fourier transforms for
, Universitext, Springer, Berlin, 2004, 236 pages (ISBN: 3-540-20665-5) | DOI | MR | Zbl
, Universitext, Springer, New York, 1992, 263 pages (ISBN: 0-387-97709-0) | DOI | MR | Zbl
Gauss-Manin systems, Brieskorn lattices and Frobenius structures. I in Proceedings of the International Conference in Honor of Frédéric Pham (Nice, 2002) , Ann. Inst. Fourier (Grenoble), Volume 53 (2003), pp. 1055-1116 http://aif.cedram.org/item?id=AIF_2003__53_4_1055_0 (ISSN: 0373-0956) | DOI | Numdam | MR | Zbl
, Annals of Math. Studies, 131, Princeton Univ. Press, Princeton, NJ, 1993, 157 pages (ISBN: 0-691-00049-2) | DOI | MR | Zbl
, Topological field theory, primitive forms and related topics (Kyoto, 1996) (Progr. Math.), Volume 160, Birkhäuser, 1998, pp. 141-175 | DOI | MR | Zbl
, Integrable systems and algebraic geometry (Kobe/Kyoto, 1997), World Sci. Publ., River Edge, NJ, 1998, pp. 107-155 | MR | Zbl
Towards mirror symmetry for varieties of general type, Adv. Math., Volume 308 (2017), pp. 208-275 (ISSN: 0001-8708) | DOI | MR
, Modern Birkhäuser Classics, Birkhäuser, 2008, 523 pages (reprint of the 1994 edition) (ISBN: 978-0-8176-4770-4) | MR | Zbl
Intersection homology. II, Invent. math., Volume 72 (1983), pp. 77-129 (ISSN: 0020-9910) | DOI | MR | Zbl
, CBMS Regional Conference Series in Mathematics, 114, Amer. Math. Soc., Providence, RI, 2011, 317 pages (ISBN: 978-0-8218-5232-3) | DOI | MR | Zbl
Hypergeometric functions and toric varieties, Funktsional. Anal. i Prilozhen., Volume 23 (1989), pp. 12-26 (ISSN: 0374-1990) | DOI | MR | Zbl
Generalized Euler integrals and
Rings of invariants of tori, Cohen-Macaulay rings generated by monomials, and polytopes, Ann. of Math., Volume 96 (1972), pp. 318-337 (ISSN: 0003-486X) | DOI | MR | Zbl
Equivariant
Limits of families of Brieskorn lattices and compactified classifying spaces, Adv. Math., Volume 223 (2010), pp. 1155-1224 (ISSN: 0001-8708) | DOI | MR | Zbl
, Progress in Math., 236, Birkhäuser, 2008, 407 pages (ISBN: 978-0-8176-4363-8) | DOI | MR | Zbl
Quantum Serre theorem as a duality between quantum
An integral structure in quantum cohomology and mirror symmetry for toric orbifolds, Adv. Math., Volume 222 (2009), pp. 1016-1079 (ISSN: 0001-8708) | DOI | MR | Zbl
Quantum cohomology and periods, Ann. Inst. Fourier (Grenoble), Volume 61 (2011), pp. 2909-2958 http://aif.cedram.org/item?id=AIF_2011__61_7_2909_0 (ISSN: 0373-0956) | DOI | Numdam | MR | Zbl
, Representation theory and complex analysis (Lecture Notes in Math.), Volume 1931, Springer, Berlin, 2008, pp. 137-234 | DOI | MR | Zbl
, From Hodge theory to integrability and TQFT tt*-geometry (Proc. Sympos. Pure Math.), Volume 78, Amer. Math. Soc., Providence, RI, 2008, pp. 87-174 | DOI | MR | Zbl
, The moduli space of curves (Texel Island, 1994) (Progr. Math.), Volume 129, Birkhäuser, 1995, pp. 335-368 | DOI | MR | Zbl
, Grundl. math. Wiss., 292, Springer, Berlin, 1994, 512 pages (ISBN: 3-540-51861-4) | MR | Zbl
, Chapman & Hall/CRC, Boca Raton, FL, 2006, 229 pages (ISBN: 978-1-58488-184-1; 1-58488-184-4) |
Quantum
Homological methods for hypergeometric families, J. Amer. Math. Soc., Volume 18 (2005), pp. 919-941 (ISSN: 0894-0347) | DOI | MR | Zbl
, Graduate Texts in Math., 227, Springer, New York, 2005, 417 pages (ISBN: 0-387-22356-8) | MR | Zbl
Rational curves on hypersurfaces (after A. Givental), Séminaire Bourbaki, vol. 1997/1998, exposé no 848, Astérisque, Volume 252 (1998), pp. 307-340 (ISSN: 0303-1179) | Numdam | MR | Zbl
, Progress in Math., 2, Birkhäuser, 1979, 339 pages (ISBN: 3-7643-3002-3) | MR | Zbl
, Singularities, Part 2 (Arcata, Calif., 1981) (Proc. Sympos. Pure Math.), Volume 40, Amer. Math. Soc., Providence, RI, 1983, pp. 319-333 | MR | Zbl
La descente des cols par les onglets de Lefschetz, avec vues sur Gauss-Manin, Astérisque, Volume 130 (1985), pp. 11-47 (ISSN: 0303-1179) | Numdam | MR | Zbl
Laurent polynomials, GKZ-hypergeometric systems and mixed Hodge modules, Compos. Math., Volume 150 (2014), pp. 911-941 (ISSN: 0010-437X) | DOI | MR | Zbl
Logarithmic Frobenius manifolds, hypergeometric systems and quantum
Fourier-Laplace transform of a variation of polarized complex Hodge structure, J. reine angew. Math., Volume 621 (2008), pp. 123-158 (ISSN: 0075-4102) | DOI | MR | Zbl
Non-commutative Hodge structures, Ann. Inst. Fourier (Grenoble), Volume 61 (2011), pp. 2681-2717 http://aif.cedram.org/item?id=AIF_2011__61_7_2681_0 (ISSN: 0373-0956) | DOI | Numdam | MR | Zbl
Modules de Hodge polarisables, Publ. Res. Inst. Math. Sci., Volume 24 (1988), pp. 849-995 (ISSN: 0034-5318) | DOI | MR | Zbl
On the structure of Brieskorn lattice, Ann. Inst. Fourier (Grenoble), Volume 39 (1989), pp. 27-72 (ISSN: 0373-0956) | DOI | Numdam | MR | Zbl
Mixed Hodge modules, Publ. Res. Inst. Math. Sci., Volume 26 (1990), pp. 221-333 (ISSN: 0034-5318) | DOI | MR | Zbl
Hypergeometric
Duality and monodromy reducibility of
Cité par Sources :