Author:
Lee Sanghyeon,Li Mu-Lin,Oh Jeongseok
Abstract
AbstractBy the reduced component in a moduli space of stable quasimaps to n-dimensional projective space $$\mathbb {P}^n$$
P
n
we mean the closure of the locus in which the domain curves are smooth. As in the moduli space of stable maps, we prove the reduced component is smooth in genus 2, degree$$\ge 3$$
≥
3
. Then we prove the virtual fundamental cycle of the moduli space of stable quasimaps to a complete intersectionXin $$\mathbb {P}^n$$
P
n
of genus 2, degree $$\ge 3$$
≥
3
is explicitly expressed in terms of the fundamental cycle of the reduced component of $$\mathbb {P}^n$$
P
n
and virtual cycles of lower genus $$<2$$
<
2
moduli spaces of X.
Publisher
Springer Science and Business Media LLC
Reference43 articles.
1. Battistella, L., Carocci, F., Manolache, C.: Reduced invariants from cuspidal maps. Trans. Am. Math. Soc. 373 , 6713–6756 (2020). arXiv:1801.07739
2. Battistella, L., Carocci, F.: A smooth compactification of the space of genus two curves in projective space via logarithmic geometry and Gorenstein curves. Geom. Topol. arXiv:2008.13506
3. Chang, H.-L., Guo, S., Li, J.: Polynomial structure of Gromov-Witten potential of quintic 3-folds. Ann. Math. 194, 585–645 (2021). arXiv:1809.11058
4. Chang, H.-L., Guo, S., Li, J.: BCOV’s Feynman rule of quintic 3-folds. arXiv:1810.00394
5. Chang, H.-L., Guo, S., Li, J., Li, W.-P.: The theory of N-mixed-spin-P fields. Geom. Topol. 25, 775–811 (2021). arXiv:1809.08806