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Regular version of the site
Of all publications in the section: 28
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Article
Maciel J., Bogomolov F. A. Central European Journal of Mathematics. 2009. No. 7:1. P. 61-65.
Article
Tikhomirov A. S., Markushevich D., Trautmann G. Central European Journal of Mathematics. 2012. Vol. 19. No. 4. P. 1331-1355.
We announce some results on compactifying moduli spaces of rank 2 vector bundles on surfaces by spaces of vector vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so-called bubbling of vector bundled connections an in differential geometry. The new moduli spaces are algebraic spaces arising as quotients by group actions according surfaces to a result of Kollár. As an example, the compactification of the space of stable rank 2 vector bundles with Chern classes $c_1=0, c_2=2$ on the projective plane is studied in more detail. Proofs are only indicated and will appear in separate papers.
Article
Bogomolov F. A., Tschinkel Y. Central European Journal of Mathematics. 2009. No. 7:3. P. 382-386.
Article
Bogomolov F. A., Rovinsky M. Central European Journal of Mathematics. 2013. Vol. 11. No. 1. P. 17-26.

Let Ψ be the projectivization (i.e., the set of one-dimensional vector subspaces) of a vector space of dimension ≥ 3 over a field. Let H be a closed (in the pointwise convergence topology) subgroup of the permutation group GΨ of the set Ψ. Suppose that H contains the projective group and an arbitrary self-bijection of Ψ transforming a triple of collinear points to a non-collinear triple. It is well-known from [9] that if Ψ is finite then H contains the alternating subgroup AΨ of GΨ.

We show in Theorem 3.1 below that H = GΨ, if Ψ is infinite.

Article
Markushevich D., Tikhomirov A. S., Verbitsky M. Central European Journal of Mathematics. 2012. Vol. 10. No. 4. P. 1185-1187.
Article
Tikhomirov A. S., Markushevich D., Verbitsky M. Central European Journal of Mathematics. 2012. Vol. 10. No. 4. P. 1185-1187.
In this preface we give a short description of the current issue of the Central European Journal of Mathematics containing 22 papers which spin around the topics of the conference “Instantons in complex geometry”, held on March 14–18, 2011 in Moscow. The main goal of the conference was to bring together specialists in complex algebraic and analytic geometries whose research interests belong to this composite area between gauge theory, moduli spaces, derived categories, vector bundles and coherent sheaves. Besides the most relevant contributions to the conference, the issue contains miscellaneous articles by other authors that fit by subject and spirit.
Article
Katzarkov L., Yotov M., Orlov D. O. et al. Central European Journal of Mathematics. 2009. No. 7:4.
Article
Przyjalkowski V. Central European Journal of Mathematics. 2011. Vol. 9. No. 5. P. 972-977.
Article
Verbitsky M. Central European Journal of Mathematics. 2011. Vol. 9. No. 3. P. 535-557.
Article
Kuznetsov A. G. Central European Journal of Mathematics. 2012. Vol. 10. No. 4. P. 1198-1231.

We introduce the notion of an instanton bundle on a Fano threefold of index 2. For such bundles we give an analogue of a monadic description and discuss the curve of jumping lines. The cases of threefolds of degree 5 and 4 are considered in a greater detail.

Article
Bogomolov F. A., Böhning C., Graf von Bothmer H. Central European Journal of Mathematics. 2012. Vol. 10. No. 2. P. 466-520.

Let G be one of the groups SL n(ℂ), Sp 2n(ℂ), SO m(ℂ), O m(ℂ), or G 2. For a generically free G-representation V, we say that N is a level of stable rationality for V/G if V/G × ℙ N is rational. In this paper we improve known bounds for the levels of stable rationality for the quotients V/G. In particular, their growth as functions of the rank of the group is linear for G being one of the classical groups.

Article
Tikhomirov A. S., Bruzzo U., Markushevich D. Central European Journal of Mathematics. 2012. Vol. 10. No. 4. P. 1232-1245.

Symplectic instanton vector bundles on the projective space $\mathbb{P}^3$ constitute a natural generalization of mathematical instantons of rank-2. We study the moduli space $I_{n;r}$ of rank-$2r$ symplectic instanton vector bundles on $\mathbb{P}^3$ with $r\ge2$ and second Chern class $n\ge r, n\equiv r(\mod 2)$. We introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus $I_{n;r}^*$ of tame symplectic instantons is irreducible and has the expected dimension, equal to $4n(r+1)-r(2r+1)$.

Article
Tschinkel Y., Bogomolov F. A. Central European Journal of Mathematics. 2008. No. 6:3. P. 343-350.
Article
Drozd Y., Gavran V. Central European Journal of Mathematics. 2014. Vol. 12. No. 5. P. 675-687.

We generalize the results of Kahn about a correspondence between Cohen-Macaulay modules and vector bundles to non-commutative surface singularities. As an application, we give examples of non-commutative surface singularities which are not Cohen-Macaulay finite, but are Cohen-Macaulay tame.

Article
Arzhantsev I., Bazhov I. Central European Journal of Mathematics. 2013. Vol. 11. No. 10. P. 1713-1724.

Let X be an affine toric variety. The total coordinates on X provide a canonical presentation !X -> X of X as a quotient of a vector space !X by a linear action of a quasitorus. We prove that the orbits of the connected component of the automorphism group Aut(X) on X coincide with the Luna strata defined by the canonical quotient presentation.

Article
Bogomolov F. A., Prokhorov Y. Central European Journal of Mathematics. 2013. Vol. 11. No. 12. P. 2099-2105.

We discuss the problem of stable conjugacy of finite subgroups of Cremona groups. We show that the group $H^1(G,Pic(X))$ is a stable birational invariant and compute this group in some cases.

Article
Bogomolov F. A., Kulikov V. S. Central European Journal of Mathematics. 2012. Vol. 10. No. 2. P. 521-529.

We show that the diffeomorphic type of the complement to a line arrangement in a complex projective plane P 2 depends only on the graph of line intersections if no line in the arrangement contains more than two points in which at least two lines intersect. This result also holds for some special arrangements which do not satisfy this property. However it is not true in general, see [Rybnikov G., On the fundamental group of the complement of a complex hyperplane arrangement, Funct.

Article
Bogomolov F. A., Kulikov V. S. Central European Journal of Mathematics. 2013. Vol. 11. No. 2. P. 254-263.
The article contains a new proof that the Hilbert scheme of irreducible surfaces of degree m in ℙ m+1 is irreducible except m = 4. In the case m = 4 the Hilbert scheme consists of two irreducible components explicitly described in the article. The main idea of our approach is to use the proof of Chisini conjecture [Kulikov Vik. S., On Chisini's conjecture II, Izv. Math., 2008, 72(5), 901-913 (in Russian)] for coverings of projective plane branched in a special class of rational curves.
Article
Bogomolov F. A., Zarhin Y. Central European Journal of Mathematics. 2009. No. 7:2. P. 206-213.
Let $\bbk$ be a field of characteristic zero and $G$ be a finite group of automorphisms of projective plane over $\bbk$. Castelnuovo's criterion implies that the quotient of projective plane by $G$ is rational if the field $\bbk$ is algebraically closed. In this paper we prove that $\mathbb{P}^2_{\bbk} / G$ is rational for an arbitrary field $\bbk$ of characteristic zero.