The spaces of rational curves on del Pezzo threefolds of degree one

The irreducibility of the spaces of rational curves on del Pezzo manifolds

“…The results about the number of components and their dimensions are known in various cases: smooth Fano hypersurfaces of certain degree ranges in [15], [11], [3], [32], [9], homogeneous varieties in [37], [18], Toric varieties in [7], [8], del Pezzo surfaces in [35], [36], [4], smooth Fano threefold in [24], [27], [5], [33], [10], del Pezzo fibrations in [22], [26], and so on.…”

The spaces of rational curves on del Pezzo threefolds of degree one

“…Acknowledgements: This work is based on the first author's Master's thesis [Shi21] at Kumamoto University. The authors would like to thank Brian Lehmann for helpful discussions and comments on an early draft of this paper.…”