Expand all Collapse all | Results 1 - 4 of 4 |
1. CMB 2011 (vol 54 pp. 430)
Complete Families of Linearly Non-degenerate Rational Curves We prove that every complete family of linearly non-degenerate
rational curves of degree $e > 2$ in $\mathbb{P}^{n}$ has at most $n-1$
moduli. For $e = 2$ we prove that such a family has at most $n$
moduli. The general method involves exhibiting a map from the base of
a family $X$ to the Grassmannian of $e$-planes in $\mathbb{P}^{n}$ and
analyzing the resulting map on cohomology.
Categories:14N05, 14H10 |
2. CMB 2009 (vol 52 pp. 161)
A New Tautological Relation in $\overline{\mathcal{M}}_{3,1}$ via the Invariance Constraint A new tautological relation of $\overline{\mathcal{M}}_{3,1}$ in codimension 3
is derived and proved, using an invariance constraint from
our previous work.
Category:14H10 |
3. CMB 2008 (vol 51 pp. 519)
The Effective Cone of the Kontsevich Moduli Space In this paper we prove that the cone of effective divisors on the
Kontsevich moduli spaces of stable maps, $\Kgnb{0,0}(\PP^r,d)$,
stabilize when $r \geq d$. We give a complete characterization of the
effective divisors on $\Kgnb{0,0}(\PP^d,d)$. They are non-negative
linear combinations of boundary divisors and the divisor of maps with
degenerate image.
Categories:14D20, 14E99, 14H10 |
4. CMB 2000 (vol 43 pp. 162)
Moduli Spaces of Polygons and Punctured Riemann Spheres The purpose of this note is to give a simple combinatorial
construction of the map from the canonically compactified moduli
spaces of punctured complex projective lines to the moduli spaces
$\P_r$ of polygons with fixed side lengths in the Euclidean space
$\E^3$. The advantage of this construction is that one can obtain a
complete set of linear relations among the cycles that generate
homology of $\P_r$. We also classify moduli spaces of pentagons.
Categories:14D20, 18G55, 14H10 |