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pro vyhledávání: '"Soldatenkov, A. P."'
Autor:
Soldatenkov, Andrey, Verbitsky, Misha
Let $(M, \Omega)$ be a holomorphically symplectic manifold equipped with a holomorphic Lagrangian fibration $\pi: M \to B$, and $\eta$ a closed $(1,1)$-form on $B$. Then $\Omega+ \pi^* \eta$ is a holomorphically symplectic form on a complex manifold
Externí odkaz:
http://arxiv.org/abs/2407.07867
The ample cone of a compact Kahler $n$-manifold $M$ is the intersection of its Kahler cone and the real subspace generated by integer (1,1)-classes. Its isotropic boundary is the set of all points $\eta$ on its boundary such that $\int_M \eta^n=0$. W
Externí odkaz:
http://arxiv.org/abs/2402.11697
A rigid cohomology class on a complex manifold is a class that is represented by a unique closed positive current. The positive current representing a rigid class is also called rigid. For a compact Kahler manifold $X$ all eigenvectors of hyperbolic
Externí odkaz:
http://arxiv.org/abs/2303.11362
Autor:
Soldatenkov, Andrey
One of the main tools for the study of compact hyperk\"ahler manifolds is the natural action of the Looijenga-Lunts-Verbitsky Lie algebra on the cohomology of such manifolds. This also applies to the mildly singular holomorphic symplectic varieties -
Externí odkaz:
http://arxiv.org/abs/2209.11029
Autor:
Ivan V. Soldatenkov
Publikováno v:
Галактика медиа: журнал медиа исследований, Vol 6, Iss 1, Pp 43-76 (2024)
During the first decades of the 21st century, social media has emerged as one of the most significant means of mass communication. Concurrently, the technological features of new media have transformed communication processes. This article addresses
Externí odkaz:
https://doaj.org/article/5dd03fe6deb147329297cbf722583de7
Autor:
Soldatenkov, Andrey, Verbitsky, Misha
A C-symplectic structure is a complex-valued 2-form which is holomorphically symplectic for an appropriate complex structure. We prove an analogue of Moser's isotopy theorem for families of C-symplectic structures and list several applications of thi
Externí odkaz:
http://arxiv.org/abs/2109.00935
Autor:
Soldatenkov, Andrey
Publikováno v:
Math. Res. Lett. 28 (2021), no. 2, 623-635
The purpose of this note is to give an account of a well-known folklore result: the Hodge structure on the second cohomology of a compact hyperk\"ahler manifold uniquely determines Hodge structures on all higher cohomology groups. We discuss the prec
Externí odkaz:
http://arxiv.org/abs/1905.07793
Autor:
Soldatenkov, Andrey
Let $X_1$ and $X_2$ be deformation equivalent projective hyperk\"ahler manifolds. We prove that the Andr\'e motive of $X_1$ is abelian if and only if the Andr\'e motive of $X_2$ is abelian. Applying this to manifolds of $\mbox{K3}^{[n]}$, generalized
Externí odkaz:
http://arxiv.org/abs/1904.11320
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