TY - JOUR
T1 - Moduli spaces of rational curves on Fano threefolds
AU - Beheshti, Roya
AU - Lehmann, Brian
AU - Riedl, Eric
AU - Tanimoto, Sho
N1 - Publisher Copyright:
© 2022 The Author(s)
PY - 2022/10/29
Y1 - 2022/10/29
N2 - We prove several classification results for the components of the moduli space of rational curves on a smooth Fano threefold. In particular, we prove a conjecture of Batyrev on the growth of the number of components as the degree increases. The key to our approach is Geometric Manin's Conjecture which predicts the number of components parameterizing free curves.
AB - We prove several classification results for the components of the moduli space of rational curves on a smooth Fano threefold. In particular, we prove a conjecture of Batyrev on the growth of the number of components as the degree increases. The key to our approach is Geometric Manin's Conjecture which predicts the number of components parameterizing free curves.
KW - Batyrev's Conjecture
KW - Fano threefolds
KW - Geometric Manin's Conjecture
KW - Moduli spaces of rational curves
UR - https://www.scopus.com/pages/publications/85134841204
U2 - 10.1016/j.aim.2022.108557
DO - 10.1016/j.aim.2022.108557
M3 - Article
AN - SCOPUS:85134841204
SN - 0001-8708
VL - 408
JO - Advances in Mathematics
JF - Advances in Mathematics
M1 - 108557
ER -