Betti numbers of stable map spaces to Grassmannians

BETTI NUMBERS FOR p STABLE IDEALS

Minimal Graded Betti Numbers and Stable Ideals

Let k be a field, and let R = k[x1, x2, x3]. Given a Hilbert function H for a cyclic module over R, we give an algorithm to produce a stable ideal I such that R/I has Hilbert function H and uniquely minimal graded Betti numbers among all R/J with the same Hilbert function, where J is another stable ideal in R. We also show that such an algorithm is impossible in more variables and disprove a re...

On Betti Numbers between the Moduli Spaces of Stable Maps and Branchvarieties

Let M0,n(r, d) be the coarse moduli space of stable maps of degree d from npointed genus 0 nodal curves to Pr. Let B0,n(r, d) be the coarse moduli space of n-pointed branchvarieties of Pr with reduced and connected 1-dimensional domain and fixed Hilbert polynomial h(m) = dm+1. In [AL06], we prove that there is a surjective birational (small) morphism φ : M0,n(r, d) −→ B0,n(r, d). In this paper,...

The First Betti Numbers of Certain Locally Trivial Fibre Spaces

The purpose of this department is to provide early announcement of significant new results, with some indications of proof. Although ordinarily a research announcement should be a brief summary of a paper to be published in full elsewhere, papers giving complete proofs of results of exceptional interest are also solicited. Manuscripts more than eight typewritten double spaced pages long will no...

Some remarks on Betti numbers of random polygon spaces

Polygon spaces such as M = {(u1, . . . , un) ∈ S1 × . . . S1,∑ni=1 liui = 0}/SO(2), or the three-dimensional analogs N play an important rôle in geometry and topology, and are also of interest in robotics where the li model the lengths of robot arms. When n is large, one can assume that each li is a positive real valued random variable, leading to a randommanifold. The complexity of such manifo...