## Publications

7 results found

Arbesfeld N, 2022, K-theoretic descendent series for Hilbert schemes of points on surfaces, *Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)*, Vol: 18, Pages: 1-16, ISSN: 1815-0659

We study the holomorphic Euler characteristics of tautological sheaves on Hilbert schemes of points on surfaces. In particular, we establish the rationality of K-theoretic descendent series. Our approach is to control equivariant holomorphic Euler characteristics over the Hilbert scheme of points on the affine plane. To do so, we slightly modify a Macdonald polynomial identity of Mellit.

Arbesfeld N, 2021, K-theoretic Donaldson–Thomas theory and the Hilbert scheme of points on a surface, *Algebraic Geometry*, Pages: 587-625

Arbesfeld N, Johnson D, Lim W,
et al., 2021, The virtual K-theory of Quot schemes of surfaces, *Journal of Geometry and Physics*, Vol: 164, Pages: 1-36, ISSN: 0393-0440

We study virtual invariants of Quot schemes parametrizing quotients of dimension atmost 1 of the trivial sheaf of rank N on nonsingular projective surfaces. We conjecturethat the generating series of virtual K-theoretic invariants are given by rational functions.We prove rationality for several geometries including punctual quotients for all surfacesand dimension 1 quotients for surfaces X with pg > 0. We also show that the generatingseries of virtual cobordism classes can be irrational.Given a K-theory class on X of rank r, we associate natural series of virtual Segre andVerlinde numbers. We show that the Segre and Verlinde series match in the followingcases:(i) Quot schemes of dimension 0 quotients,(ii) Hilbert schemes of points and curves over surfaces with pg > 0,(iii) Quot schemes of minimal elliptic surfaces for quotients supported on fiber classes.Moreover, for punctual quotients of the trivial sheaf of rank N, we prove a new symmetryof the Segre/Verlinde series exchanging r and N. The Segre/Verlinde statements haveanalogues for punctual Quot schemes over curves.

Arbesfeld N, Enriquez B, 2015, ON A LOWER CENTRAL SERIES FILTRATION OF THE GROTHENDIECK-TEICHMULLER LIE ALGEBRA grt<sub>1</sub>, *MOSCOW MATHEMATICAL JOURNAL*, Vol: 15, Pages: 205-256, ISSN: 1609-3321

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- Citations: 1

Arbesfeld N, 2013, Partial permutations avoiding pairs of patterns, *DISCRETE MATHEMATICS*, Vol: 313, Pages: 2614-2625, ISSN: 0012-365X

Arbesfeld N, Schiffmann O, 2012, A presentation of the deformed W_{1+\infty} algebra, *Proceedings of the conference Infinite Analysis 11—Frontier of Integrability held at the University of Tokyo, Tokyo, July 25–29, 2011, and the conference "Symmetries, Integrable Systems and Representations'' held at the Université Claude Bernard Lyon 1, Lyon, December 13–16, 2011.*

We provide a generators and relation description of the deformedW_{1+\infty}-algebra introduced in previous joint work of E. Vasserot and thesecond author. This gives a presentation of the (spherical) cohomological Hallalgebra of the one-loop quiver, or alternatively of the spherical degeneratedouble affine Hecke algebra of GL(\infty).

Arbesfeld N, Jordan D, 2010, New results on the lower central series quotients of a free associative algebra, *JOURNAL OF ALGEBRA*, Vol: 323, Pages: 1813-1825, ISSN: 0021-8693

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- Citations: 8

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