Related papers: Geometric Invariant Theory based on Weil Divisors

This is the second part of the paper "A degeneration of stable morphisms and relative stable morphisms", (math.AG/0009097). In this paper, we constructed the relative Gromov-Witten invariants of a pair of a smooth variety and a smooth…

We prove a conjecture of Buch and Mihalcea in the case of the incidence variety X=Fl(1,n-1;n) and determine the structure of its (T-equivariant) quantum K-theory ring. Our results are an interplay between geometry and combinatorics. The…

We describe genus g>1 potentials of semisimple Frobenius structures. Our formula can be considered as a definition in the axiomatic context of Frobenius manifolds. In Gromov-Witten theory, it becomes a conjecture expressing higher genus…

Let N be a nilpotent Lie group and let S be an invariant geometric structure on N (cf. symplectic, complex or hypercomplex). We define a left invariant Riemannian metric on N compatible with S to be "minimal", if it minimizes the norm of…

We introduce and study equivariant Hilbert series of ideals in polynomial rings in countably many variables that are invariant under a suitable action of a symmetric group or the monoid $Inc(\mathbb{N})$ of strictly increasing functions.…

We describe Mui invariants in terms of Milnor operations and give a simple proof for Mui's theorem on rings of invariants of polynomial tensor exterior algebras with respect to the action of finite general linear groups. Moreover, we…

For a nonconstant holomorphic map between projective Riemann surfaces with conformal metrics, we consider invariant Schwarzian derivatives and projective Schwarzian derivatives of general virtual order. We show that these two quantities are…

In this paper, we study the Gromov-Witten theory of the Hilbert schemes X^{[n]} of points on smooth projective surfaces X with positive geometric genus p_g. Using cosection localization technique due to Y. Kiem and J. Li [KL1, KL2], we…

Let G be a connected reductive algebraic group and let G'=[G,G] be its derived subgroup. Let (G,V) be a multiplicity free representation with a one dimensional quotient (see definition below). We prove that the algebra D(V)^{G'} of…

Let $\cl{M}$ be a Hilbert module of holomorphic functions over a natural function algebra $\mathcal{A}(\Omega)$, where $\Omega \subseteq \bb{C}^m$ is a bounded domain. Let $\cl{M}_0\subseteq \cl{M}$ be the submodule of functions vanishing…

We construct an open enumerative theory for the Landau-Ginzburg (LG) model $(\mathbb{C}^2, \mu_r\times \mu_s, x^r+y^s)$. The invariants are defined as integrals of multisections of a Witten bundle with descendents over a moduli space that…

Let $G$ and $\tilde G$ be connected complex reductive Lie groups, $G$ semisimple. Let $\Lambda^+$ be the monoid of dominant weights for a positive root system $\Delta^+$, and let $l(w)$ be the length of a Weyl group element $w$. Let…

We introduce the notion of Zwiebach invariants that generalize Gromov-Witten invariants and homotopical algebra structures. We outline the induction procedure that induces the structure of Zwiebach on the subbicomplex, that gives the…

We show that, for both the conformal and projective groups, all the differential invariants of a generic surface in three-dimensional space can be written as combinations of the invariant derivatives of a single differential invariant. The…

Given a finite group $G$, we define a new invariant of odd-dimensional oriented closed manifolds and call it the KDW invariant. This invariant is a Dijkgraaf--Witten invariant in terms of $K$-theory. In this paper, we compute the invariant…

Given an algebraic surface $X$, the Hilbert scheme $X^{[n]}$ of $n$-points on $X$ admits a contraction morphism to the $n$-fold symmetric product $X^{(n)}$ with the extremal ray generated by a class $\beta_n$ of a rational curve. We…

We extend the notion of generalized Whittaker models by allowing them to be built upon smooth irreducible representations of unipotent subgroups of a $p$-adic reductive group that are not necessarily characters, nor induced from Weil…

This paper studies separating invariants: mappings on $D$ dimensional domains which are invariant to an appropriate group action, and which separate orbits. The motivation for this study comes from the usefulness of separating invariants in…

The Gromov-Witten theory of Deligne-Mumford stacks is a recent development, and hardly any computations have been done beyond 3-point genus 0 invariants. This paper provides explicit recursions which, together with some invariants computed…

We consider the 2-generated free metabelian associative and Lie algebras over the complex field and the invariants of the dihedral groups of finite order acting on these algebras. In the associative case we find a finite set of generators…