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This article is cited in 5 scientific papers (total in 5 papers)
$\mathrm P=\mathrm W$ Phenomena
L. Katzarkovab, V. V. Przyjalkowskicb, A. Harderd a University of Miami
b National Research University "Higher School of Economics", Moscow
c Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
d Lehigh University
Abstract:
In this paper, we describe recent work towards the mirror $\mathrm P=\mathrm W$ conjecture, which relates the weight filtration on the cohomology of a log Calabi–Yau manifold to the perverse Leray filtration on the cohomology of the homological mirror dual log Calabi–Yau manifold taken with respect to the affinization map. This conjecture extends the classical relationship between Hodge numbers of mirror dual compact Calabi–Yau manifolds, incorporating tools and ideas which appear in the fascinating and groundbreaking works of de Cataldo, Hausel, and Migliorini [1] and de Cataldo and Migliorini [2]. We give a broad overview of the motivation for this conjecture, recent results towards it, and describe how this result might arise from the SYZ formulation of mirror symmetry. This interpretation of the mirror $\mathrm P=\mathrm W$ conjecture provides a possible bridge between the mirror $\mathrm P=\mathrm W$ conjecture and the well-known $\mathrm P=\mathrm W$ conjecture in non-Abelian Hodge theory.
Keywords:
$\mathrm P=\mathrm W$ conjecture, mixed Hodge structure, perverse Leray filtration, mirror symmetry.
Received: 06.06.2019 Revised: 26.09.2019
Citation:
L. Katzarkov, V. V. Przyjalkowski, A. Harder, “$\mathrm P=\mathrm W$ Phenomena”, Mat. Zametki, 108:1 (2020), 33–46; Math. Notes, 108:1 (2020), 39–49
Linking options:
https://www.mathnet.ru/eng/mzm12795https://doi.org/10.4213/mzm12795 https://www.mathnet.ru/eng/mzm/v108/i1/p33
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Abstract page: | 442 | Full-text PDF : | 60 | References: | 53 | First page: | 12 |
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