Related papers: On the generalized Futaki invariant

Let $G$ be a connected, complex reductive Lie group and $X$ a $\mathbb Q$-Fano $G$-spherical variety. In this paper we compute the weighed non-Archimedean functionals of a $G$-equivariant normal test configurations of $X$ via combinatory…

We continue the study, begun in [Kouno-Naito-Orr-Sagaki, 2021], of inverse Chevalley formulas for the equivariant $K$-group of semi-infinite flag manifolds. Using the language of alcove paths, we reformulate and extend our combinatorial…

We construct and analyse models of equivariant cohomology for differentiable stacks with Lie group actions extending classical results for smooth manifolds due to Borel, Cartan and Getzler. We also derive various spectral sequences for the…

In this paper we extend the notion of Futaki invariant to big and nef classes in such a way that it defines a continuous function on the \K\ cone up to the boundary. We apply this concept to prove that reduced normal crossing singularities…

We develop the diffeomorphism invariant Colombeau-type algebra of nonlinear generalized functions in a modern and compact way. Using a unifying formalism for the local setting and on manifolds, the construction becomes simpler and more…

The article presents four reasons why the elliptic genus is the most general characteristic class that admits a generalization to singular spaces. We prove that the elliptic characteristic class (with an additional factor) is essentially…

Using Quot schemes and a localization theorem we study Gromov-Witten invariants for partial flag varieties. The strategy is to extend A. Bertram's result of Gromov-Witten invariants for special Schubert varieties of Grassmannians to the…

In a previous paper Affine symmetries of the equivariant quantum cohomology of rational homogeneous spaces, a general formula was given for the multiplication by some special Schubert classes in the quantum cohomology of any homogeneous…

Using the Okounkov-Maulik stable map, we identify the equivariant cohomology of instanton moduli spaces with the space of polynomials on an infinite number of variables. We define the generalized Jack polynomials as the polynomials…

Here we propose a way to construct generalized Kostka polynomials. Namely, we construct an equivariant filtration on tensor products of irreducible representations. Further, we discuss properties of the filtration and the adjoint graded…

Let $A(t)$ be a continuous path of Fredhom operators, we first prove that the spectral flow $sf(A(t))$ is cogredient invariant. Based on this property, we give a decomposition formula of spectral flow if the path is invariant under a…

This paper is devoted to the study of generalized differentiation properties of the infimal convolution. This class of functions covers a large spectrum of nonsmooth functions well known in the literature. The subdifferential formulas…

This paper generalizes the easy addition formula. Given a normal variety $X$ with an invertible sheaf $L$, inequalities are found bounding $\ka(X,L)$ from above based on the behavior of $L$ restricted to a subvariety or to a pair of…

We follow the lead of Bocci and Chiantini and show how differences in the invariant alpha can be used to classify certain classes of subschemes of P^3. Specifically, we will seek to classify arithmetically Cohen-Macaulay codimension 2…

This article is an expanded version of talks given by the authors in Oberwolfach, Bochum, and at the Fano Conference in Torino. Some new results (e. g. the material concerning flag varieties, Quot spaces over $\P^1$, and the generalized…

Group algebras of permutations have proved highly useful in solving a number of problems in large N gauge theories. I review the use of permutations in classifying gauge invariants in one-matrix and multi-matrix models and computing their…

Fano varieties are 'atomic pieces' of algebraic varieties, the shapes that can be defined by polynomial equations. We describe the role of computation and database methods in the construction and classification of Fano varieties, with an…

In this work we prove a residue formula for Morita-Futaki-Bott invariant with respect any holomorphic vector fields with isolated (possibly degenerated) singularities in terms of Grothendieck's residues.

The aim of this paper is to give a generalization of the theory equivariant functions, initiated in [17, 4], to arbitrary subgroups of PSL2(R). We show that there is a deep relation between the geometry of these groups and some analytic and…

We introduce a generalization of the Dijkgraaf-Witten invariants for cusped or compact oriented 3-manifolds. We show that the generalized DW invariants distinguish some pairs of cusped hyperbolic 3-manifolds with the same hyperbolic volumes…