Gröbner geometry of Schubert polynomials

A Knutson, E Miller - Annals of Mathematics, 2005 - JSTOR
Given a permutation, we consider a determinantal ideal whose generators are certain
minors in the generix n× n matrix (filled with independent variables). Using'multidegrees' as …

Four positive formulae for type A quiver polynomials

A Knutson, E Miller, M Shimozono - Inventiones mathematicae, 2006 - Springer
We give four positive formulae for the (equioriented type A) quiver polynomials of Buch and
Fulton [BF99]. All four formulae are combinatorial, in the sense that they are expressed in …

Characteristic classes of orbit stratifications, the axiomatic approach

LM Fehér, R Rimányi, A Weber - … Conference on the Trends in Schubert …, 2017 - Springer
Consider a complex algebraic group G acting on a smooth variety M with finitely many orbits,
and let Ω be an orbit. The following three invariants of Ω ⊂ M can be characterized …

Schur and Schubert polynomials as Thom polynomials—cohomology of moduli spaces

L Fehér, R Rimányi - Open Mathematics, 2003 - degruyter.com
The theory of Schur and Schubert polynomials is revisited in this paper from the point of view
of generalized Thom polynomials. When we apply a general method to compute Thom …

On the cohomological Hall algebra of Dynkin quivers

R Rimányi - arxiv preprint arxiv:1303.3399, 2013 - arxiv.org
Consider the Cohomological Hall Algebra as defined by Kontsevich and Soibelman,
associated with a Dynkin quiver. We reinterpret the geometry behind the multiplication map …

The general quadruple point formula

R Marangell, R Rimányi - American journal of mathematics, 2010 - muse.jhu.edu
Maps between manifolds $ M^ m\to N^{m+\ell} $($\ell0 $) have multiple points, and more
generally, multisingularities. The closure of the set of points where the map has a particular …

Geometry of fibers of the multiplication map of deep linear neural networks

SIP Lehalleur, R Rimányi - arxiv preprint arxiv:2411.19920, 2024 - arxiv.org
We study the geometry of the algebraic set of tuples of composable matrices which multiply
to a fixed matrix, using tools from the theory of quiver representations. In particular, we …

Equivariant classes of matrix matroid varieties

LM Fehér, A Némethi, R Rimányi - Commentarii Mathematici Helvetici, 2012 - ems.press
To each subset I of f1;:::; kg associate an integer rI/. Denote by X the collection of those nk
matrices for which the rank of a union of columns corresponding to a subset I is rI/, for all I …

Quiver polynomials in iterated residue form

R Rimanyi - Journal of Algebraic Combinatorics, 2014 - Springer
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A formula for non-equioriented quiver orbits of type A

AS Buch, R Rimányi - arxiv preprint math/0412073, 2004 - arxiv.org
We prove a positive combinatorial formula for the equivariant class of an orbit closure in the
space of representations of an arbitrary quiver of type $ A $. Our formula expresses this …