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Of all publications in the section: 433
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Working paper
Gritsenko V. arxiv.org. math. Cornell University, 2012. No. 6503.
The fake monster Lie algebra is determined by the Borcherds function Phi_{12} which is the reflective modular form of the minimal possible weight with respect to O(II_{2,26}). We prove that the first non-zero Fourier-Jacobi coefficient of Phi_{12} in any of 23 Niemeier cusps is equal to the Weyl-Kac denominator function of the affine Lie algebra of the root system of the corresponding Niemeier lattice. This is an automorphic answer (in the case of the fake monster Lie algebra) on the old question of I. Frenkel and A. Feingold (1983) about possible relations between hyperbolic Kac-Moody algebras, Siegel modular forms and affine Lie algebras.
Working paper
Mayanskiy E. arxiv.org. math. Cornell University, 2013. No. 5150.
We list all finite abelian groups which act effectively on smooth cubic fourfolds.
Working paper
Vladimir Lebedev. arxiv.org. math. Cornell University, 2011. No. 1112.4892v1.
We obtain a partial solution of the problem on the growth of the norms of exponential functions with a continuous phase in the Wiener algebra. The problem was posed by J.-P. Kahane at the International Congress of Mathematicians in Stockholm in 1962. He conjectured that (for a nonlinear phase) one can not achieve the growth slower than the logarithm of the frequency. Though the conjecture is still not confirmed, the author obtained first nontrivial results.
Working paper
Kurnosov N. arxiv.org. math. Cornell University, 2015
We prove that a generic complex deformation of a generalized Kummer variety contains no complex analytic tori.
Working paper
Feigin B. L., Makhlin I. arxiv.org. math. Cornell University, 2015
We present a new combinatorial formula for Hall-Littlewood functions associated with the affine root system of type A~n−1, i.e. corresponding to the affine Lie algebra slˆn. Our formula has the form of a sum over the elements of a basis constructed by Feigin, Jimbo, Loktev, Miwa and Mukhin in the corresponding irreducible representation.Our formula can be viewed as a weighted sum of exponentials of integer points in a certain infinite-dimensional convex polyhedron. We derive a weighted version of Brion's theorem and then apply it to our polyhedron to prove the formula.
Working paper
Alexey Elagin. arxiv.org. math. Cornell University, 2016. No. 1610.02325.
We fi nd a criterion for an eff ective divisor D on a smooth surface to be left-orthogonal or strongly left-orthogonal (i.e. for the pair of line bundles (O;O(D)) to be exceptional or strong exceptional).
Working paper
Verbitsky M. arxiv.org. math. Cornell University, 2010. No. 1003.3174.
Let M be a G2-manifold. We consider an almost CR-structure on the sphere bundle of unit tangent vectors on M, called the CR twistor space. This CR-structure is integrable if and only if M is a holonomy G2 manifold. We interpret G2-instanton bundles as CR-holomorphic bundles on its twistor space.
Working paper
Galkin S., Karzhemanov I., Shinder E. arxiv.org. math. Cornell University, 2016. No. 1602.06107.
On the projective plane there is a unique cubic root of the canonical bundle and this root is acyclic. On fake projective planes such root exists and is unique if there are no 3-torsion divisors (and usually exists but not unique otherwise). Earlier we conjectured that any such cubic root (assuming it exists) must be acyclic. In the present note we give a new short proof of this statement and show acyclicity of some other line bundles on those fake projective planes with at least 9 automorphisms. Similarly to our earlier work we employ simple representation theory for non-abelian finite groups. The novelty stems from the idea that if some line bundle is non-linearizable with respect to a finite abelian group, then it should be linearized by a finite (non-abelian) Heisenberg group. Our argument also exploits J. Rogawski's vanishing theorem and the linearization of an auxiliary line bundle.
Working paper
M.V. Karasev. arxiv.org. math. Cornell University, 2014. No. 1404.1790v2.
For slow–fast quantum systems, we compute first corrections to the quantum action and to the effective slow Hamiltonian.
Working paper
Ivan Cheltsov, Park J., Won J. arxiv.org. math. Cornell University, 2013
We show that affine cones over smooth cubic surfaces do not admit non-trivial $\mathbb{G}_a$ -actions.
Working paper
Busjatskaja I., Kochetkov Y. arxiv.org. math. Cornell University, 2016. No. 1607.05325.
A non-degenerate two-dimentional linear operator Ф  transforms the unit circle into ellipse.We define the coefficient of deformation k(Ф), as the relation of the lendth of the smaller ellipses axis to its bigger one. In this work we compute the mean value of k(Ф).Analogously, we define the deformation coefficient  k(Ф) in three-dimensional case and give an estimation of its mean value.
Working paper
Chistyakov Vyacheslav V. arxiv.org. math. Cornell University, 2011. No. 1112.5561v1.
The notion of a (metric) modular on an arbitrary set and the corresponding modular space, more general than a metric space, were introduced and studied recently by the author [V.V. Chistyakov, Metric modulars and their application, Dokl. Math. 73 (1) (2006) 32–35, and Modular metric spaces, I: Basic concepts, Nonlinear Anal. 72 (1) (2010) 1–14]. In this paper we establish a fixed point theorem for contractive maps in modular spaces. It is related to contracting rather “generalized average velocities” than metric distances, and the successive approximations of fixed points converge to the fixed points in a weaker sense as compared to the metric convergence.
Working paper
Timorin V., Khovanskii A. G. arxiv.org. math. Cornell University, 2013. No. 1305.4484.
We prove a version of the Aleksandrov-Fenchel inequality for mixed volumes of coconvex bodies. This version is motivated by an inequality from commutative algebra relating intersection multiplicities of ideals.
Working paper
Izosimov A. arxiv.org. math. Cornell University, 2013
In 1970s, a method was developed for integration of nonlinear equations by means of algebraic geometry. Starting from a Lax representation with a spectral parameter, the algebro-geometric method allows to solve the system explicitly in terms of Theta functions of Riemann surfaces. However, the explicit formulas obtained in this way fail to answer such natural topological questions as whether a given singular solution is stable or not. In the present paper, the problem of stability for equilibrium points is considered, and it is shown that this problem can also be approached by means of algebraic geometry.
Working paper
Vladimir L. Popov. arxiv.org. math. Cornell University, 2017. No. 1707.06914 [math.AG].
We classify all connected affine algebraic groups G such that there are only finitely many G-orbits in every algebraic G-variety containing a dense open G-orbit. We also prove that G enjoys this property if and only if every irreducible algebraic G-variety X is modality-regular, i.e., the modality of X (in the sense of V. Arnol’d) equals to that of a family which is open in X.
Working paper
Positselski L. arxiv.org. math. Cornell University, 1995. No. alg-geom/9507014.
It is proved that any strictly exceptional collection generating the derived category of coherent sheaves on a smooth projective variety X with \rk K_0(X) = \dim X + 1 constists of locally free sheaves up to a common shift.
Working paper
Durand B., Shen A., Vereshchagin N. arxiv.org. math. Cornell University, 2012. No. 2896.
We describe all Ammann tilings of a plane, a half-plane and a quadrant. In our description, every tiling is associated to an infinite sequence of two letters. We provide simple criteria of (a) whether a tiling associated with a sequence tiles the entire plane, a half-plane or a quadrant and (b) whether tiling associated with two sequences are congruent. It is well known that all Ammann tilings are aperiodic; we show how one can use this fact to construct an aperiodic 2-dimensional sub-shift of finite type
Working paper
Rovinsky M. arxiv.org. math. Cornell University, 2016
Let K be a field and G be a group of its automorphisms. If K is algebraic over the subfield KG fixed by G then, according to Hilbert's Theorem 90, any smooth (i.e. with open stabilizers) K-semilinear representation of the group G is isomorphic to a direct sum of copies of K. If K is not algebraic over KG then there exist non-semisimple smooth semilinear representations of G over K, so Hilbert's Theorem 90 does not hold. Let now G be the group of all permutations of an infinite set S acting naturally on the field k(S) freely generated over a subfield k by the set S. The goal of this note is to present three examples of G-invariant subfields K\subseteq k(S) such that the smooth K-semilinear representations of G of {\sl finite length} admit an explicit description, close to Hilbert's Theorem 90. Namely, (i) if K=k(S) then any smooth K-semilinear representation of G of finite length is isomorphic to a direct sum of copies of K, (ii) if K\subset k(S) is the subfield of rational homogeneous functions of degree 0 then any smooth K-semilinear representation of G of finite length splits into a direct sum of one-dimensional K-semilinear representations of G, (iii) if K\subset k(S) is the subfield generated over k by x-y for all x,y\in S then there is a unique isomorphism class of indecomposable smooth K-semilinear representations of G of each given finite length.