arXiv subjects

Pedro Magalhães

Publications and source records attributed to Pedro Magalhães.

3 recordsLinked to original sources

arXiv2026

Products in absolute Hodge cohomology and mixed Hodge formality

Given a complex algebraic variety, we relate the product structure on its absolute Hodge cohomology with mixed Hodge formality, a notion of formality in the sense of rational homotopy, that takes into account the mixed Hodge structures present in complex algebraic geometry. Namely, we prove that mixed Hodge formality implies the splitting of absolute Hodge cohomology as a square-zero extension. We define and study certain products, akin to Massey products, which live in the absolute Hodge cohomology and obstruct its splitting. We also relate mixed Hodge formality to the existence of multiplicative Chow-Künneth decompositions.

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arXiv2026

Mixed Hodge formality

We introduce the notion of mixed Hodge formality, which refines classical formality and takes into account the mixed Hodge structures present on the cohomology of complex algebraic varieties. We develop an obstruction theory for mixed Hodge formality, witnessing the non-triviality of extensions of mixed Hodge structures. This allows us to understand the non-formality of certain compact Kähler manifolds in the mixed Hodge sense.

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arXiv2026

The inflation functor in pluripotential homological algebra

We introduce a functor from cochain complexes to bicomplexes, called inflation functor, which sends quasi-isomorphisms to the class of pluripotential weak equivalences. We show this functor is part of a Quillen adjunction. Its right adjoint is a well-known construction in complex geometry, which gives a sheaf-theoretic presentation of Bott-Chern and Aeppli cohomologies. The inflation functor plays a key role in pluripotential Koszul duality theory for operads and allows us to construct the infinity-category of bicomplexes in the pluripotential sense.

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