A Desingularization of the Main Component of the Moduli Space of Genus-One Stable Maps into $\Bbb{P}^n$

Details A Desingularization of the Main Component of the Moduli Space of Genus-One Stable Maps into $\Bbb{P}^n$ A Desingularization of the Main Component of the Moduli Space of Genus-One Stable Maps into $\Bbb{P}^n$

2006-03-14

arxiv.org/abs/math/0603353v2

Mathematics

Algebraic Geometry

revised version; 13 figures

Scientific paper

We construct a desingularization of the ``main component'' $\bar{\mathfrak M}_{1,k}^0(\Bbb{P}^n,d)$ of the moduli space $\bar{\mathfrak M}_{1,k}(\Bbb{P}^n,d)$ of genus-one stable maps into the complex projective space $\Bbb{P}^n$. As a bonus, we obtain desingularizations of certain natural sheaves over $\bar{\mathfrak M}_{1,k}^0(\Bbb{P}^n,d)$. Such desingularizations are useful for integrating natural cohomology classes on $\bar{\mathfrak M}_{1,k}^0(\Bbb{P}^n,d)$ using localization. In turn, these classes can be used to compute the genus-one Gromov-Witten invariants of complete intersections and classical enumerative invariants of projective spaces involving genus-one curves. The desingularization of $\bar{\mathfrak M}_{1,k}^0(\Bbb{P}^n,d)$ is obtained by sequentially blowing up $\bar{\mathfrak M}_{1,k}(\Bbb{P}^n,d)$ along ``bad'' subvarieties. At the end of the process, we are left with a modification of the main component, which turns out to be nonsingular.

Affiliated with

Also associated with

No associations

Rating

A Desingularization of the Main Component of the Moduli Space of Genus-One Stable Maps into $\Bbb{P}^n$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Desingularization of the Main Component of the Moduli Space of Genus-One Stable Maps into $\Bbb{P}^n$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Desingularization of the Main Component of the Moduli Space of Genus-One Stable Maps into $\Bbb{P}^n$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-728940