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pro vyhledávání: '"Zheglov, Alexander"'
Autor:
Zheglov, Alexander
Let $K$ be a field of characteristic zero, let $A_1=K[x][\partial ]$ be the first Weyl algebra. In this paper we prove that the Dixmier conjecture for the first Weyl algebra is true, i.e. each algebra endomorphism of the algebra $A_1$ is an automorph
Externí odkaz:
http://arxiv.org/abs/2410.06959
Autor:
Zheglov, Alexander
The notion of quasi-elliptic rings appeared as a result of an attempt to classify a wide class of commutative rings of operators found in the theory of integrable systems, such as rings of commuting differential, difference, differential-difference,
Externí odkaz:
http://arxiv.org/abs/2205.06790
Autor:
Guo, Junhu, Zheglov, Alexander
Let $K$ be a field of characteristic zero, let $A_1=K[x][\partial ]$ be the first Weyl algebra. In this paper we prove the following two results. Assume there exists a non-zero polynomial $f(X,Y)\in K[X,Y]$, which has a non-trivial solution $(P,Q)\in
Externí odkaz:
http://arxiv.org/abs/2203.13343
Autor:
Kulikov, Viktor S., Zheglov, Alexander
In this paper we construct first examples of smooth projective surfaces of general type satisfying the following conditions: there are 1) an ample integral curve $C$ with $C^2=1$ and $h^0(X,O_X(C))=1$; \quad 2) a divisor $D$ with $(D, C)_X=g(C)-1$, $
Externí odkaz:
http://arxiv.org/abs/1710.05991
Autor:
Burban, Igor, Zheglov, Alexander
In this paper, we study properties of the algebras of planar quasi-invariants. These algebras are Cohen-Macaulay and Gorenstein in codimension one. Using the technique of matrix problems, we classify all Cohen-Macaulay modules of rank one over them a
Externí odkaz:
http://arxiv.org/abs/1703.01762
Autor:
Burban, Igor, Zheglov, Alexander
In this article, we describe the spectral sheaves of algebras of commuting differential operators of genus one and rank two with singular spectral curve, solving a problem posed by Previato and Wilson. We also classify all indecomposable semi-stable
Externí odkaz:
http://arxiv.org/abs/1602.08694
In this paper we study rank two commuting ordinary differential operators with polynomial coefficients and the orbit space of the automorphisms group of the first Weyl algebra on such operators. We prove that for arbitrary fixed spectral curve of gen
Externí odkaz:
http://arxiv.org/abs/1503.00485
Autor:
Kurke, Herbert, Zheglov, Alexander
We investigate further alebro-geometric properties of commutative rings of partial differential operators continuing our research started in previous articles. In particular, we start to explore the most evident examples and also certain known exampl
Externí odkaz:
http://arxiv.org/abs/1405.5114
Publikováno v:
Selecta Math. (N.S.), 20:4 (2014), 1159-1195
Several algebro-geometric properties of commutative rings of partial differential operators as well as several geometric constructions are investigated. In particular, we show how to associate a geometric data by a commutative ring of partial differe
Externí odkaz:
http://arxiv.org/abs/1211.0976
Publikováno v:
International Journal of Mathematics,Volume: 21, Issue: 6(2010) pp. 755-797
We investigate Picard functor of a formal punctured ribbon. We prove that under some conditions this functor is representable by a formal group scheme. Formal punctured ribbons were introduced in arXiv:0708.0985.
Comment: 42 pages, minor changes
Comment: 42 pages, minor changes
Externí odkaz:
http://arxiv.org/abs/0901.1607