[-modules et dualité de Serre quantiques dans le secteur troit]
Étant donnée une variété ou une orbifold non compacte , on définit un sous-espace naturel de la cohomologie de que nous appelons cohomologie étroite. On montre qu’en dépit du fait que est non compacte, il existe un couplage non-dégénéré sur ce sous-espace. Cette cohomologie étroite s’avère utile pour l’étude de la théorie de Gromov–Witten en genre 0. Lorsque est une variété complexe lisse ou un champ de Deligne–Mumford lisse, on peut définir un -module quantique sur sa cohomologie étroite. Ceci nous amène à une nouvelle formulation de la dualité de Serre quantique.
Given a non-compact manifold or orbifold, we define a natural subspace of the cohomology of called the narrow cohomology. We show that despite being non-compact, there is a well-defined and non-degenerate pairing on this subspace. The narrow cohomology proves useful for the study of genus zero Gromov–Witten theory. When is a smooth complex variety or Deligne–Mumford stack, one can define a quantum -module on the narrow cohomology of . This yields a new formulation of quantum Serre duality.
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Keywords: Gromov–Witten theory, quantum D-modules, quantum Serre duality, mirror symmetry
Mot clés : théorie de Gromov–Witten, D-modules quantiques, dualité de Serre quantique, symétrie miroir
@article{AIF_2021__71_3_1135_0,
author = {Shoemaker, Mark},
title = {Narrow quantum $D$-modules and quantum {Serre} duality},
journal = {Annales de l'Institut Fourier},
pages = {1135--1183},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {71},
number = {3},
year = {2021},
doi = {10.5802/aif.3419},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.3419/}
}
TY - JOUR AU - Shoemaker, Mark TI - Narrow quantum $D$-modules and quantum Serre duality JO - Annales de l'Institut Fourier PY - 2021 SP - 1135 EP - 1183 VL - 71 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.3419/ DO - 10.5802/aif.3419 LA - en ID - AIF_2021__71_3_1135_0 ER -
%0 Journal Article %A Shoemaker, Mark %T Narrow quantum $D$-modules and quantum Serre duality %J Annales de l'Institut Fourier %D 2021 %P 1135-1183 %V 71 %N 3 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.3419/ %R 10.5802/aif.3419 %G en %F AIF_2021__71_3_1135_0
Shoemaker, Mark. Narrow quantum $D$-modules and quantum Serre duality. Annales de l'Institut Fourier, Tome 71 (2021) no. 3, pp. 1135-1183. doi : 10.5802/aif.3419. http://www.numdam.org/articles/10.5802/aif.3419/
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