?
An inequality for Betti numbers of hyper-Kähler manifolds of dimension 6
Mathematical notes. 2016. Vol. 99. No. 1. P. 330–334.
Kurnosov N.
Pavlov A., Mathematische Zeitschrift 2021 No. 297 P. 223–254
We show that for maximal Cohen–Macaulay modules over the homogeneous coordinate ring of a smooth Calabi–Yau varieties X, the computation of Betti numbers can be reduced to computations of dimensions of certain HomHom spaces in the bounded derived category Db(X). In the simplest case of a smooth elliptic curve E embedded in P2 as a smooth cubic, we get explicit values for Betti ...
Added: October 31, 2020
Buryak A., Moscow Mathematical Journal 2012 Vol. 12 No. 1 P. 1–17
In this paper we give a formula for the classes (in the Grothendieck ring of complex quasi-projective varieties) of irreducible components of (1,k)-quasi-homogeneous Hilbert schemes of points on the plane. We find a new simple geometric interpretation of the q,t-Catalan numbers. Finally, we investigate a connection between (1,k)-quasi-homogeneous Hilbert schemes and homogeneous nested Hilbert schemes. ...
Added: October 1, 2020
Buryak A., Feigin B. L., , in: Symmetries, Integrable Systems and RepresentationsVol. 40: Symmetries, Integrable Systems and Representations.: Springer, 2013.
In this paper we prove that the generating series of the Poincare polynomials of quasihomogeneous Hilbert schemes of points in the plane has a beautiful decomposition into an infinite product. We also compute the generating series of the numbers of quasihomogeneous components in a moduli space of sheaves on the projective plane. The answer is ...
Added: September 30, 2020
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
Pavlov A., Journal of Algebra 2019 Vol. 526 P. 211–242
We apply Orlov's equivalence to derive formulas for the Betti numbers of maximal Cohen-Macaulay modules over the cone an elliptic curve $(E,x)$ embedded into $\mathbb{P}^{n-1}$, by the full linear system $|\mathcal{O}(nx)|$, for $n>3$. The answers are given in terms of recursive sequences. These results are applied to give a criterion of (Co-)Koszulity.
In the last two ...
Added: May 24, 2019
Grantcharov G., Verbitsky Misha, Communications in Contemporary Mathematics 2013 Vol. 15 No. 2 P. 1–27
We describe a family of calibrations arising naturally on a hyper-Kähler manifold M. These calibrations calibrate the holomorphic Lagrangian, holomorphic isotropic and holomorphic coisotropic subvarieties. When M is an HKT (hyper-Kähler with torsion) manifold with holonomy SL(n, H), we construct another family of calibrations Φi, which calibrates holomorphic Lagrangian and holomorphic coisotropic subvarieties. The calibrations ...
Added: March 27, 2013