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Spectral Sequences for Cyclic Homology
P. 99–129.
We prove the non-commutative Hodge-to-de Rham Degeneration Conjecture of Kontsevich and Soibelman.
Krichever I., Грушевский С., Нортон Х., Успехи математических наук 2019 Т. 74 № 2(446) С. 81–148
We study the behaviour of real-normalized (RN) meromorphic differentials on Riemann surfaces under degeneration. We describe all possible limits of RN differentials on any stable curve. In particular we prove that the residues at the nodes are solutions of a suitable Kirchhoff problem on the dual graph of the curve. We further show that the ...
Added: October 31, 2019
Galkin S., / Series math "arxiv.org". 2018. No. 1809.02737.
Given a singular variety I discuss the relations between quantum cohomology of its resolution and smoothing. In particular, I explain how toric degenerations helps with computing Gromov--Witten invariants, and the role of this story in Fanosearch programme. The challenge is to formulate enumerative symplectic geometry of complex 3-folds in a way suitable for extracting invariants ...
Added: September 25, 2018
Makhlin I., Algebraic Combinatorics 2019 P. 305–322
We present a combinatorial monomial basis (or, more precisely, a family of monomial bases) in every finite-dimensional irreducible so2n+1-module. These bases are in many ways similar to the FFLV bases for types A and C. They are also defined combinatorially via sums over Dyck paths in certain triangular grids. Our sums, however, involve weights depending on the length of ...
Added: August 30, 2018
Ilten N. O., Lewis J., Victor Przyjalkowski, Journal of Algebra 2013 Vol. 374 P. 104–121
We show that every Picard rank one smooth Fano threefold has a weak Landau–Ginzburg model coming from a toric degeneration. The fibers of these Landau–Ginzburg models can be compactified to K3 surfaces with Picard lattice of rank 19. We also show that any smooth Fano variety of arbitrary dimension which is a complete intersection of ...
Added: July 2, 2013
Feigin E., Selecta Mathematica, New Series 2012 Vol. 18 No. 3 P. 513–537
Let Fλ be a generalized flag variety of a simple Lie group G embedded into the projectivization of an irreducible G-module Vλ. We define a flat degeneration Fλa, which is a GaM variety. Moreover, there exists a larger group Ga acting on Fλa, which is a degeneration of the group G. The group Ga contains ...
Added: August 31, 2012