Torification and factorization of birational maps

D Abramovich, K Karu, K Matsuki… - Journal of the American …, 2002 - ams.org
Building on work of the fourth author and Morelli's work, we prove the weak factorization
conjecture for birational maps in characteristic zero: a birational map between complete …

Hirzebruch classes and motivic Chern classes for singular spaces

JP Brasselet, J Schürmann, S Yokura - Journal of Topology and …, 2010 - World Scientific
In this paper we study some new theories of characteristic homology classes of singular
complex algebraic (or compactifiable analytic) spaces. We introduce a motivic Chern class …

Motivic Chern classes and K‐theoretic stable envelopes

LM Feher, R Rimanyi, A Weber - Proceedings of the London …, 2021 - Wiley Online Library
We consider a smooth algebraic variety with an action of a linear algebraic group acting with
finitely many orbits. We study equivariant characteristic classes of the orbits, namely the …

Discriminants in the Grothendieck ring

R Vakil, MM Wood - 2015 - projecteuclid.org
We consider the limiting behavior of discriminants, by which we mean informally the locus in
some parameter space of some type of object where the objects have certain singularities …

Elliptic classes of Schubert varieties via Bott–Samelson resolution

R Rimányi, A Weber - Journal of Topology, 2020 - Wiley Online Library
Based on recent advances on the relation between geometry and representation theory, we
propose a new approach to elliptic Schubert calculus. We study the equivariant elliptic …

ħ-Deformed Schubert Calculus in Equivariant Cohomology, K-Theory, and Elliptic Cohomology

R Rimányi - Singularities and Their Interaction with Geometry and …, 2021 - Springer
In this survey paper we review recent advances in the calculus of Chern-Schwartz-
MacPherson, motivic Chern, and elliptic classes of classical Schubert varieties. These three …

Algebraic elliptic cohomology theory and flops I

M Levine, Y Yang, G Zhao, J Riou - Mathematische Annalen, 2019 - Springer
We define the algebraic elliptic cohomology theory coming from Krichever's elliptic genus as
an oriented cohomology theory on smooth varieties over an arbitrary perfect field. We show …

Elliptic classes of Schubert varieties

S Kumar, R Rimányi, A Weber - Mathematische Annalen, 2020 - Springer
We introduce new notions in elliptic Schubert calculus: the (twisted) Borisov–Libgober
classes of Schubert varieties in general homogeneous spaces G/P. While these classes do …

Nonabelian shift operators and shifted Yangians

S Tamagni - arXiv preprint arXiv:2412.17906, 2024 - arxiv.org
We introduce nonabelian analogs of shift operators in the enumerative theory of quasimaps.
We apply them on the one hand to strengthen the emerging analogy between enumerative …

Elliptic genera, real algebraic varieties and quasi-Jacobi forms

A Libgober - Topology of stratified spaces, 2011 - books.google.com
We survey the push-forward formula for elliptic class and various applications obtained in
the papers by L. Borisov and the author. We then discuss the ring of quasi-Jacobi forms …