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On the irreducibility of Hilbert scheme of surfaces of minimal degree
Central European Journal of Mathematics. 2013. Vol. 11. No. 2. P. 254-263.
Bogomolov F. A., Kulikov V. S.
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.
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 ...
Added: October 10, 2012
Fedor Bogomolov, Rovinsky M., / Cornell University. Series math "arxiv.org". 2012.
Let $\Psi$ be the projectivization (i.e., the set of one-dimensional vector
subspaces) of a vector space of dimension $\ge 3$ over a field. Let $H$ be a
closed (in the pointwise convergence topology) subgroup of the permutation
group $\mathfrak{S}_{\Psi}$ of the set $\Psi$. Suppose that $H$ contains the
projective group and an arbitrary self-bijection of $\Psi$ transforming a
triple of ...
Added: November 21, 2014
М. : ЦЭМИ РАН, 2011
Conference covers both fundamental problems ofthe theory, and application to research of complex organizational and technical systems. ...
Added: June 6, 2013
NY : Springer, 2013
This volume contains a selection of contributions from the "First International Conference in Network Analysis," held at the University of Florida, Gainesville, on December 14-16, 2011. The remarkable diversity of fields that take advantage of Network Analysis makes the endeavor of gathering up-to-date material in a single compilation a useful, yet very difficult, task. The ...
Added: December 19, 2012
Pham S. K., Antipov D., Sirotkin Alexander et al., Journal of Computational Biology 2013 Vol. 20 No. 4 P. 359-371
One of the key advances in genome assembly that has led to a significant improvement in contig lengths has been improved algorithms for utilization of paired reads (mate-pairs). While in most assemblers, mate-pair information is used in a post-processing step, the recently proposed Paired de Bruijn Graph (PDBG) approach incorporates the mate-pair information directly in ...
Added: March 21, 2014
Bezrukavnikov R., Finkelberg M. V., Cambridge Journal of Mathematics 2014 Vol. 2 No. 2 P. 163-190
Marc Haiman has reduced Macdonald Positivity Conjecture to a statement about geometry of the Hilbert scheme of points on the plane, and formulated a generalization of the conjecture where the symmetric group is replaced by the wreath product of S_n and Z/rZ. He has proven the original conjecture by establishing the geometric statement about the ...
Added: December 20, 2014
Galkin S., Shinder E., / Cornell University. 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
Prokhorov Y., Kuznetsov A., Shramov K., Japanese Journal of Mathematics 2018 Vol. 13 No. 1 P. 109-185
We discuss various results on Hilbert schemes of lines and conics and automorphism groups of smooth Fano threefolds of Picard rank 1. Besides a general review of facts well known to experts, the paper contains some new results, for instance, we give a description of the Hilbert scheme of conics on any smooth Fano threefold ...
Added: November 22, 2017
Braverman A., Michael Finkelberg, / Cornell University. Series math "arxiv.org". 2014.
In this note, we extend the results of arxiv:1111.2266 and arxiv:1203.1583 to the non simply laced case. To this end we introduce and study the twisted zastava spaces. ...
Added: February 5, 2015
Akhtar M., Coates T., Galkin S. et al., / Cornell University. Series math "arxiv.org". 2012. No. 1212.1785.
Given a Laurent polynomial f, one can form the period of f: this is a function of one complex variable that plays an important role in mirror symmetry for Fano manifolds. Mutations are a particular class of birational transformations acting on Laurent polynomials in two variables; they preserve the period and are closely connected with ...
Added: September 14, 2013
Prokhorov Y., Journal of Algebraic Geometry 2012 Vol. 21 No. 3 P. 563-600
We classify all finite simple subgroups of the Cremona group Cr3(C). ...
Added: September 19, 2012
Vassiliev V., Труды Математического института им. В.А. Стеклова РАН 2015 Т. 290 С. 211-225
The naturally topologized order complex of proper algebraic subsets in RP^2, defined by systems of quadratic forms, has rational homology of S^13. ...
Added: January 19, 2016
Vologodsky V., Finkelberg M. V., Bezrukavnikov R., Cambridge Journal of Mathematics 2014 Vol. 2 No. 2 P. 163-190
Marc Haiman has reduced Macdonald Positivity Conjecture to a statement about geometry of the Hilbert scheme of points on the plane, and formulated a generalization of the conjecture where the symmetric group is replaced by the wreath product of S_n and Z/rZ. He has proven the original conjecture by establishing the geometric statement about the ...
Added: December 17, 2015
Fesler R., / Cornell University. Series arXiv "math". 2023.
We are building a theory of simple Hurwitz numbers for the reflection groups B and D parallel to the classical theory for the symmetric group. We also study analogs of the cut-and-join operators. An algebraic description of Hurwitz numbers and an explicit formula for them in terms of Schur polynomials are provided. We also relate ...
Added: September 9, 2023
F.A. Bogomolov, Vik.S. Kulikov, / Cornell University. Series math "arxiv.org". 2014.
In \cite{Ku0}, the ambiguity index $a_{(G,O)}$ was introduced for each
equipped finite group $(G,O)$. It is equal to the number of connected
components of a Hurwitz space parametrizing coverings of a projective line with
Galois group $G$ assuming that all local monodromies belong to conjugacy
classes $O$ in $G$ and the number of branch points is greater than some
constant. ...
Added: November 21, 2014
Bezrukavnikov R., Finkelberg M. V., / Cornell University. Series math "arxiv.org". 2012. No. 1208.3696.
Mark Haiman has reduced Macdonald positivity conjecture to a statement about geometry of the Hilbert scheme of points on the plane, and formulated a generalization of the conjectures where the symmetric group is replaced by the wreath product $S_n\ltimes (Z/r Z)^n$. He has proven the original conjecture by establishing the geometric statement about the Hilbert ...
Added: February 6, 2013
Galkin S., Popov P., / Cornell University. Series math "arxiv.org". 2018. No. 1810.07001.
Let X(n) denote n-th symmetric power of a cubic surface X. We show that X(4)×X is stably birational to X(3)×X, despite examples when X(4) is not stably birational to X(3). ...
Added: October 19, 2018
М. : МАКС Пресс, 2017
The collection represents proceedings of the XVIII international conference “Problems of Theoretical Cybernetics” (Penza, 19–23 June, 2017), that is sponsored by Russian Foundation for Basic Research (project N 17-01-20217-г). The conference subject area includes: control systems synthesis, complexity, reliability, and diagnostics; automata; computer languages and programming; graph theory; combinatorics; coding theory; theory of pattern recognition; ...
Added: August 25, 2017
Popov P., / Cornell University. Series math "arxiv.org". 2018. No. 1810.04563.
We study relations in the Grothendieck ring of varieties which connect the Hilbert scheme of points on a cubic hypersurface Y with a certain moduli space of twisted cubic curves on Y. These relations are generalizations of the "beautiful" Y-F(Y) relation by Galkin and Shinder which connects Y with the Hilbert scheme of two points on Y and the Fano variety F(Y) of lines on Y. We ...
Added: October 23, 2018
F. A. Bogomolov, Vik. S. Kulikov, European Journal of Mathematics 2015 Vol. 1 No. 4 P. 260-278
In \cite{Ku0}, the ambiguity index $a_{(G,O)}$ was introduced for each equipped finite group $(G,O)$. It is equal to the number of connected components of a Hurwitz space parametrizing coverings of a projective line with Galois group $G$ assuming that all local monodromies belong to conjugacy classes $O$ in $G$ and the number of branch points ...
Added: November 21, 2014
М. : МАКС Пресс, 2015
The collection represents proceedings of the nineth international conference "Discrete Models in Control Systems Theory" that is held by Lomonosov Moscow State Uneversity and is dedicated in 90th anniversary of Sergey Vsevolodovich Yablonsky's birth. The conference subject are includes: discrete functional systems; discrete functions properties; control systems synthesis, complexity, reliability, and diagnostics; automata; graph theory; ...
Added: March 28, 2015
Buryak A., Feigin B. L., Nakajima H., International Mathematics Research Notices 2015 Vol. 2015 No. 13 P. 4708-4715
In a recent paper the first two authors proved that the generating series of the Poincare polynomials of the quasihomogeneous Hilbert schemes of points in the plane has a simple decomposition in an infinite product. In this paper we give a very short geometrical proof of that formula. ...
Added: September 29, 2020
Kuznetsov A., Prokhorov Y., Shramov K., / Cornell University. Series arXiv "math". 2016.
We discuss various results on Hilbert schemes of lines and conics and automorphism groups of smooth Fano threefolds with Picard rank 1. Besides a general review of facts well known to experts, the paper contains some new results, for instance, we give a description of the Hilbert scheme of conics on any smooth Fano threefold ...
Added: May 16, 2016
М. : МАКС Пресс, 2017
The collection represents proceedings of the XVIII international conference “Problems of Theoretical Cybernetics” (Penza, 19–23 June, 2017), that is sponsored by Russian Foundation for Basic Research (project N 17-01-20217-г). The conference subject area includes: control systems synthesis, complexity, reliability, and diagnostics; automata; computer languages and programming; graph theory; combinatorics; coding theory; theory of pattern recognition; ...
Added: September 21, 2017