Divisors on the Space of Maps to Grassmannians

Explicit Computations for the Intersection Numbers on Grassmannians , and on the Space of Holomorphic Maps from CP 1 into

On the pointfree counterpart of the local definition of classical continuous maps

The familiar classical result that a continuous map from a space $X$ to a space $Y$ can be defined by giving continuous maps $varphi_U: U to Y$ on each member $U$ of an open cover ${mathfrak C}$ of $X$ such that $varphi_Umid U cap V = varphi_V mid U cap V$ for all $U,V in {mathfrak C}$ was recently shown to have an exact analogue in pointfree topology, and the same was done for the familiar cla...

Gromov-witten Invariants of Jumping Curves

Given a vector bundle E on a smooth projective variety X, we can define subschemes of the Kontsevich moduli space of genus-zero stable maps M0,0(X, β) parameterizing maps f : P1 → X such that the Grothendieck decomposition of f∗E has a specified splitting type. In this paper, using a “compactification” of this locus, we define Gromov-Witten invariants of jumping curves associated to the bundle ...

Gromov Invariants for Holomorphic Maps from Riemann Surfaces to Grassmannians

Two compactifications of the space of holomorphic maps of fixed degree from a compact Riemann surface to a Grassmannian are studied. It is shown that the Uhlenbeck compactification has the structure of a projective variety and is dominated by the algebraic compactification coming from the Grothendieck Quot Scheme. The latter may be embedded into the moduli space of solutions to a generalized ve...

Divisors on the Moduli Spaces of Stable Maps to Flag Varieties and Reconstruction

We determine generators for the codimension 1 Chow group of the moduli spaces of genus zero stable maps to flag varieties G/P . In the case of SL flags, we find all relations between our generators, showing that they essentially come from M0,n. In addition, we analyze the codimension 2 classes on the moduli spaces of stable maps to Grassmannians and prove a new codimension 2 relation. This will...