New relations among the genus-zero Gromov-Witten invariants of a complex projective manifold X are exhibited. When the cohomology of X is generated by divisor classes and classes “with vanishing one-point invariants,” the relations determine many-point invariants in terms of one-point invariants. 0. Introduction The localization theorem for equivariant cohomology has recently been used with gre...

We investigate the symplectic geometric and also differential aspects of moduli space connections on a compact connected Riemann surface X . Fix theta characteristic K 1 / 2 ; it defines divisor M stable vector bundles rank r degree zero. Given bundle E ? lying outside divisor, we construct natural holomorphic connection that depends holomorphically Using this connection, canonical isomorphism ...

the zero-divisor graph of a commutative ring r with respect to nilpotent elements is a simple undirected graph $gamma_n^*(r)$ with vertex set z_n(r)*, and two vertices x and y are adjacent if and only if xy is nilpotent and xy is nonzero, where z_n(r)={x in r: xy is nilpotent, for some y in r^*}. in this paper, we investigate the basic properties of $gamma_n^*(r)$. we discuss when it will be eu...

We provide: (1) an independent quantifier-free axiomatization for André’s central translation structures and state a conjecture, which, if true, would show a very strong connection between central translation structures and translation planes; (2) a first-order axiomatization of Everett’s and Permutti’s affine geometries over rings without zero divisors in which any two non-zero elements have a...

In an attempt to study the zero divisors in infinite Hopf algebras, we study two non-trivial examples of non-group ring infinite Hopf algebras and show that a variant of Kaplansky’s classical zero divisor conjecture holds for these two Hopf algebras.

Ž . Ž . Let R be a commutative ring with 1 and let Z R be its set of Ž . Ž . zero-divisors. We associate a simple graph G R to R with vertices Ž . Ž . 4 Z R * s Z R y 0 , the set of nonzero zero-divisors of R, and for disŽ . tinct x, y g Z R *, the vertices x and y are adjacent if and only if xy s 0. Ž . Thus G R is the empty graph if and only if R is an integral domain. The main object of this...