The dual Lagrangian fibration of known hyper-K\" ahler manifolds
YJ Kim - arXiv preprint arXiv:2109.03987, 2021 - arxiv.org
Given a Lagrangian fibration $\pi: X\to\mathbb {P}^ n $ of a compact hyper-K\" ahler manifold
of $\text {K3}^{[n]} $, $\text {Kum} _n $, $\text {OG10} $ or $\text {OG6} $-type, we construct a …
of $\text {K3}^{[n]} $, $\text {Kum} _n $, $\text {OG10} $ or $\text {OG6} $-type, we construct a …
Relative and absolute Lefschetz standard conjectures for some Lagrangian fibrations
G Ancona, M Cavicchi, R Laterveer, G Saccà - arXiv preprint arXiv …, 2023 - arxiv.org
We show that the hyper-K\" ahler varieties of OG10-type constructed by Laza-Sacc\a-Voisin
(LSV) verify the Lefschetz standard conjecture. This is an application of a more general …
(LSV) verify the Lefschetz standard conjecture. This is an application of a more general …
Fourier–Mukai and autoduality for compactified Jacobians. I
To every singular reduced projective curve X one can associate, following Esteves, many
fine compactified Jacobians, depending on the choice of a polarization on X, each of which …
fine compactified Jacobians, depending on the choice of a polarization on X, each of which …
Higher discriminants and the topology of algebraic maps
L Migliorini, V Shende - Algebraic Geometry, 2018 - cris.unibo.it
Given a map between algebraic varieties, we define loci in the target of the map which we
name the “higher discriminants.” They are defined in terms of transversality conditions, and …
name the “higher discriminants.” They are defined in terms of transversality conditions, and …
Fourier–Mukai and autoduality for compactified Jacobians, II
To every reduced (projective) curve X with planar singularities one can associate, following
E Esteves, many fine compactified Jacobians, depending on the choice of a polarization on …
E Esteves, many fine compactified Jacobians, depending on the choice of a polarization on …
On Chern classes of Lagrangian fibered hyper-K\" ahler manifolds
C Voisin - arXiv preprint arXiv:2305.09396, 2023 - arxiv.org
We study the rank stratification for the differential of a Lagrangian fibration over a smooth
basis. We also introduce and study the notion of Lagrangian morphism of vector bundles. As …
basis. We also introduce and study the notion of Lagrangian morphism of vector bundles. As …
Quasi-BPS categories for Higgs bundles
T Pădurariu, Y Toda - arXiv preprint arXiv:2408.02168, 2024 - arxiv.org
We introduce quasi-BPS categories for twisted Higgs bundles, which are building blocks of
the derived category of coherent sheaves on the moduli stack of semistable twisted Higgs …
the derived category of coherent sheaves on the moduli stack of semistable twisted Higgs …
Fourier-Mukai transforms and the decomposition theorem for integrable systems
D Maulik, J Shen, Q Yin - arXiv preprint arXiv:2301.05825, 2023 - arxiv.org
We study the interplay between the Fourier-Mukai transform and the decomposition theorem
for an integrable system $\pi: M\rightarrow B $. Our main conjecture is that the Fourier-Mukai …
for an integrable system $\pi: M\rightarrow B $. Our main conjecture is that the Fourier-Mukai …
Isotrivial Lagrangian fibrations of compact hyper-K\" ahler manifolds
This article initiates the study of isotrivial Lagrangian fibrations of compact hyper-K\" ahler
manifolds. We present four foundational results that extend well-known facts about isotrivial …
manifolds. We present four foundational results that extend well-known facts about isotrivial …
Stacky dualities for the moduli of Higgs bundles
R Derryberry - Advances in Mathematics, 2020 - Elsevier
The central result of this paper is an identification of the shifted Cartier dual of the moduli
stack M g (C) of G˜-Higgs bundles on C of arbitrary degree (modulo shifts by Z (G˜)) with a …
stack M g (C) of G˜-Higgs bundles on C of arbitrary degree (modulo shifts by Z (G˜)) with a …