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Semi-infinite A-variations of Hodge structure over extended Kaehler cone
International Mathematics Research Notices. 2001. Vol. 21. P. 1111–1139.
Keywords: Hodge structures
Kurnosov N., Soldatenkov A., Verbitsky M., Advances in Mathematics 2019 Vol. 351 P. 275–295
Let M be a simple hyperkähler manifold. Kuga-Satake
construction gives an embedding of H^2(M, C) into the
second cohomology of a torus, compatible with the Hodge
structure. We construct a torus T and an embedding of the
graded cohomology space H^•(M, C) → H^{•+l}(T, C) for some
l, which is compatible with the Hodge structures and the
Poincaré pairing. Moreover, this ...
Added: June 3, 2019
Efimov A., Selecta Mathematica, New Series 2018 Vol. 24 No. 4 P. 3753–3762
In this short note we study the questions of (non-)L-equivalence of algebraic varieties, in particular, for abelian varieties and K3 surfaces. We disprove the original version of a conjecture of Huybrechts stating that isogenous K3 surfaces are L-equivalent. Moreover, we give examples of derived equivalent twisted K3 surfaces, such that the underlying K3 surfaces are ...
Added: October 14, 2018
Katzarkov L. V., Kontsevich M., Pantev T., Journal of Differential Geometry 2017 Vol. 105 No. 1 P. 55–117
In this paper we prove the smoothness of the moduli space of Landau–Ginzburg models. We formulate and prove a Bogomolov–Tian–Todorov theorem for the deformations of Landau–Ginzburg models, develop the necessary Hodge theory for varieties with potentials, and prove a double degeneration statement needed for the unobstructedness result. We discuss the various definitions of Hodge numbers ...
Added: October 23, 2017
Ananʼin S., Verbitsky M., Journal de Mathématiques Pures et Appliquées 2014 Vol. 101 No. 2 P. 188–197
Let M be a compact hyperkähler manifold, and W the coarse moduli of complex deformations of M. Every positive integer class v in H^2(M) defines a divisor Dv in W consisting of all algebraic manifolds polarized by v. We prove that every connected component of this divisor is dense in W. ...
Added: January 28, 2015
Galkin S., Shinder E., / Series math "arxiv.org". 2014. No. 1405.5154.
We find a relation between a cubic hypersurface Y and its Fano variety of lines F(Y) in the Grothendieck ring of varieties. We prove that if the class of an affine line is not a zero-divisor in the Grothendieck ring of varieties, then Fano variety of lines on a smooth rational cubic fourfold is birational ...
Added: May 21, 2014
Katzarkov L., Przyjalkowski V., , in: Proceedings of the Gökova Geometry-Topology Conference 2011.: Boston: International Pre, 2012. P. 97–124.
In the last three years a new concept — the concept of wall crossing
has emerged. The current situation with wall crossing phenomena, after pa pers of Seiberg–Witten, Gaiotto–Moore–Neitzke, Vafa–Cecoti and seminal works
by Donaldson–Thomas, Joyce–Song, Maulik–Nekrasov–Okounkov–Pandharipande,
Douglas, Bridgeland, and Kontsevich–Soibelman, is very similar to the situation with
Higgs Bundles after the works of Higgs and Hitchin — it is ...
Added: February 16, 2013