Stringy Kähler Moduli for the Pfaffian–Grassmannian Correspondence
Symmetry, integrability and geometry: methods and applications, Tome 17 (2021) Cet article a éte moissonné depuis la source Math-Net.Ru

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The Pfaffian–Grassmannian correspondence relates certain pairs of derived equivalent non-birational Calabi–Yau 3-folds. Given such a pair, I construct a set of derived equivalences corresponding to mutations of an exceptional collection on the relevant Grassmannian, and give a mirror symmetry interpretation, following a physical analysis of Eager, Hori, Knapp, and Romo.
Keywords: Calabi–Yau threefolds, derived category, derived equivalence, matrix factorizations, Landau–Ginzburg model, Pfaffian, Grassmannian.
Mots-clés : stringy Kähler moduli
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     title = {Stringy {K\"ahler} {Moduli} for the {Pfaffian{\textendash}Grassmannian} {Correspondence}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a27/}
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Will Donovan. Stringy Kähler Moduli for the Pfaffian–Grassmannian Correspondence. Symmetry, integrability and geometry: methods and applications, Tome 17 (2021). http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a27/

[1] Addington N., Donovan W., Segal E., “The Pfaffian–Grassmannian equivalence revisited”, Algebr. Geom., 2 (2015), 332–364 | DOI | MR | Zbl

[2] Ballard M., Favero D., Katzarkov L., “Variation of geometric invariant theory quotients and derived categories”, J. Reine Angew. Math., 746 (2019), 235–303, arXiv: 1203.6643 | DOI | MR | Zbl

[3] Borisov L., Căldăraru A., “The Pfaffian–Grassmannian derived equivalence”, J. Algebraic Geom., 18 (2009), 201–222, arXiv: math.AG/0608404 | DOI | MR | Zbl

[4] Bridgeland T., “Flops and derived categories”, Invent. Math., 147 (2002), 613–632, arXiv: math.AG/0009053 | DOI | MR | Zbl

[5] Donovan W., Segal E., “Window shifts, flop equivalences and {G}rassmannian twists”, Compos. Math., 150 (2014), 942–978 | DOI | MR | Zbl

[6] Eager R., Hori K., Knapp J., Romo M., “Beijing lectures on the grade restriction rule”, Chin. Ann. Math. Ser. B, 38 (2017), 901–912 | DOI | MR | Zbl

[7] Halpern-Leistner D., “The derived category of a GIT quotient”, J. Amer. Math. Soc., 28 (2015), 871–912, arXiv: 1203.0276 | DOI | MR | Zbl

[8] Herbst M., Hori K., Page D., Phases of $\mathcal{N}=2$ theories in $1+1$ dimensions with boundary, arXiv: 0803.2045

[9] Hori K., “Grade restriction rule and equivalences of categories”, Kinosaki Symposium in Algebraic Geometry (Kyoto University, 2016), 75–88

[10] Hori K., Tong D., “Aspects of non-abelian gauge dynamics in two-dimensional $\mathcal N=(2,2)$ theories”, J. High Energy Phys., 2007:5 (2007), 079, 41 pp., arXiv: hep-th/0609032 | DOI | MR

[11] Kapranov M. M., “On the derived categories of coherent sheaves on some homogeneous spaces”, Invent. Math., 92 (1988), 479–508 | DOI | MR | Zbl

[12] Keating A. M., “Dehn twists and free subgroups of symplectic mapping class groups”, J. Topol., 7 (2014), 436–474, arXiv: 1204.2851 | DOI | MR | Zbl

[13] Kuznetsov A., Homological projective duality for Grassmannians of lines, arXiv: math.AG/0610957

[14] Kuznetsov A., “Exceptional collections for Grassmannians of isotropic lines”, Proc. Lond. Math. Soc., 97 (2008), 155–182, arXiv: math.AG/0512013 | DOI | MR | Zbl

[15] Rødland E. A., “The Pfaffian Calabi–Yau, its mirror, and their link to the Grassmannian $G(2,7)$”, Compositio Math., 122 (2000), 135–149, arXiv: math.AG/9801092 | DOI | MR

[16] Segal E., “Equivalence between GIT quotients of Landau–Ginzburg B-models”, Comm. Math. Phys., 304 (2011), 411–432, arXiv: 0910.5534 | DOI | MR | Zbl

[17] Segal E., Thomas R., “Quintic threefolds and Fano elevenfolds”, J. Reine Angew. Math., 743 (2018), 245–259, arXiv: 1410.6829 | DOI | MR | Zbl

[18] Seidel P., Thomas R., “Braid group actions on derived categories of coherent sheaves”, Duke Math. J., 108 (2001), 37–108, arXiv: math.AG/0001043 | DOI | MR | Zbl

[19] Shipman I., “A geometric approach to Orlov's theorem”, Compos. Math., 148 (2012), 1365–1389, arXiv: 1012.5282 | DOI | MR | Zbl

[20] Weyman J., Cohomology of vector bundles and syzygies, Cambridge Tracts in Mathematics, 149, Cambridge University Press, Cambridge, 2003 | DOI | MR | Zbl