Nesting Maps of Grassmannians

Divisors on the Space of Maps to Grassmannians

In this note we study the divisor theory of the Kontsevich moduli spacesM0,0(G(k, n), d) of genus-zero stable maps to the Grassmannians. We calculate the classes of several geometrically significant divisors. We prove that the cone of effective divisors stabilizes as n increases and we determine the stable effective cone. We also characterize the ample cone.

Filtrations, Factorizations and Explicit Formulae for Harmonic Maps

We use filtrations of the Grassmannian model to produce explicit algebraic formulae for harmonic maps of finite uniton number from a Riemann surface to the unitary group for a general class of factorizations by unitons. We show how these specialize to give explicit formulae for harmonic maps into the special orthogonal and symplectic groups, real, complex and quaternionic Grassmannians, and the...

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

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 ...

Linked Hom Spaces

In this note, we describe a theory of linked Hom spaces which complements that of linked Grassmannians. Given two chains of vector bundles linked by maps in both directions, we give conditions for the space of homomorphisms from one chain to the other to be itself represented by a vector bundle. We apply this to present a more transparent version of an earlier construction of limit linear serie...