The $P=W$ identity for isolated cluster varieties: full rank case
Zili Zhang
TL;DR
This paper establishes a deep connection between the perverse filtration of certain Lagrangian fibrations and the mixed Hodge-theoretic weight filtration for isolated cluster varieties, specifically in the full rank case.
Contribution
It provides a systematic construction of Lagrangian fibrations from integer matrices and proves the $P=W$ identity for full rank matrices in the context of isolated cluster varieties.
Findings
Perverse filtration matches the weight filtration for full rank matrices.
Constructs real analytic Lagrangian fibrations from integer matrices.
Establishes the $P=W$ identity in the full rank case.
Abstract
We initiate a systematic construction of real analytic Lagrangian fibrations from integer matrices. We prove that when the matrix is of full column rank, the perverse filtration associated with the Lagrangian fibration matches the mixed Hodge-theoretic weight filtration of the isolated cluster variety associated with the matrix.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Nonlinear Waves and Solitons