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pro vyhledávání: '"Oblomkov, A."'
The aim of this paper is to give an explicit description of the fixed loci of symplectic automorphisms for certain hyperkahler manifolds, namely for Hilbert schemes on K3 surfaces and for generalized Kummer varieties. Here we extend our previous resu
Externí odkaz:
http://arxiv.org/abs/2308.14692
Autor:
Oblomkov, Alexei, Rozansky, Lev
In our previous papers we used the Hilbert scheme of points on $C^2$ in order to construct a triply graded link homology and its $gl(m)$ version. Here we extend the $gl(m)$ construction to super-algebras $gl(m|k)$.
Comment: 17 pages, comments ar
Comment: 17 pages, comments ar
Externí odkaz:
http://arxiv.org/abs/2212.02665
Publikováno v:
Algebraic Geometry, 2024
We compute the Poincar\'e polynomials of the compactified Jacobians for plane curve singularities with Puiseaux exponents $(nd,md,md+1)$, and relate them to the combinatorics of $q,t$-Catalan numbers in the non-coprime case. We also confirm a conject
Externí odkaz:
http://arxiv.org/abs/2210.12569
Given a semisimple element in the loop Lie algebra of a reductive group, we construct a quasi-coherent sheaf on a partial resolution of the trigonometric commuting variety of the Langlands dual group. The construction uses affine Springer theory and
Externí odkaz:
http://arxiv.org/abs/2204.00303
Autor:
Oblomkov, Alexei, Rozansky, Lev
We establish an isomorphism between the Khovanov-Rozansky triply graded link homology and the geometric triply graded homology due to the authors. Hence we provide an interpretation of the Khovanov-Rozansky homology of the closure of a braid $\beta$
Externí odkaz:
http://arxiv.org/abs/2010.14546
Using new explicit formulas for the stationary GW/PT descendent correspondence for nonsingular projective toric 3-folds, we show that the correspondence intertwines the Virasoro constraints in Gromov-Witten theory for stable maps with the Virasoro co
Externí odkaz:
http://arxiv.org/abs/2008.12514
Autor:
Bottman, Nathaniel, Oblomkov, Alexei
For $r \geq 1$ and $\mathbf{n} \in \mathbb{Z}_{\geq0}^r\setminus\{\mathbf{0}\}$, we construct a proper complex variety $\overline{2M}_{\mathbf{n}}$. $\overline{2M}_{\mathbf{n}}$ is locally toric, and it is equipped with a forgetful map $\overline{2M}
Externí odkaz:
http://arxiv.org/abs/1910.02037
Autor:
Oblomkov, Alexei, Rozansky, Lev
We modify our previous construction of link homology in order to include a natural duality functor $\mathfrak{F}$. To a link $L$ we associate a triply-graded module $HXY(L)$ over the graded polynomial ring $R(L)=\mathbb{C}[x_1,y_1,\dots,x_\ell,y_\ell
Externí odkaz:
http://arxiv.org/abs/1905.06511
Autor:
Oblomkov, Alexei
These are the notes of the lectures delivered by the author at CIME in June 2018. The main purpose of the notes is to provide an overview of the techniques used in the construction of the triply graded link homology. The homology is space of global s
Externí odkaz:
http://arxiv.org/abs/1901.04052
Autor:
Oblomkov, A.
In this note we prove an integral formula for the bare one-leg PT vertex with descendents. The formula follows from the PT version of Ellingsrud-G\"ottsche-Lehn formula that is explained here. We apply the integral formula to obtain an elementary pro
Externí odkaz:
http://arxiv.org/abs/1901.03014