Conics in quintic del Pezzo varieties
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
The smooth quintic del Pezzo variety $Y$ is well-known to be obtained as a linear sections of the Grassmannian variety $\mathrm{Gr}(2,5)$ under the Pl\"ucker embedding into $\mathbb{P}^{9}$. Through a local computation, we show the Hilbert scheme of conics in $Y$ for $\text{dim} Y \ge 3$ can be obtained from a certain Grassmannian bundle by a single blowing-up/down transformation.
Abstract
The smooth quintic del Pezzo variety $Y$ is well-known to be obtained as a linear sections of the Grassmannian variety $\mathrm{Gr}(2,5)$ under the Pl\"ucker embedding into $\mathbb{P}^{9}$. Through a local computation, we show the Hilbert scheme of conics in $Y$ for $\text{dim} Y \ge 3$ can be obtained from a certain Grassmannian bundle by a single blowing-up/down transformation.
참고문헌 (13)
- J. G. Broida, "A Comprehensive Introduction to Linear Algebra" (1989), Addison-Wesley
- K. Chung, "Desingularization of Kontsevich’s compactification of twisted cubics in V5", Manuscripta Math, 171(1-2), pp.347~367 (2023)[DOI]
- K. Chung, "Double lines in the quintic del Pezzo fourfold", Bull. Korean Math. Soc, 60(2), pp.485~494 (2023)[DOI]
- K. Chung, "Geometry of moduli spaces of rational curves in linear sections of Grassmannian Gr(2, 5)", J. Pure Appl. Algebra, 222(4), pp.868~888 (2018)[DOI]
- A. Fujiki, "Supplement to “On the inverse of monoidal transformation”", Publ. Res. Inst. Math. Sci, 7, pp.637~644 (1972)[DOI]
- T. Fujita, "On the structure of polarized manifolds with total deficiency one. II", J. Math. Soc. Japan, 33(3), pp.415~434 (1981)[DOI]
- M. Furushima, "The family of lines on the Fano threefold V5", Nagoya Math. J, 116, pp.111~122 (1989)[DOI]
- A. I. Iliev, "The Fano surface of the Gushel threefold", Compositio Math, 94(1), pp.81~107 (1994)
- A. G. Kuznetsov, "Hilbert schemes of lines and conics and automorphism groups of Fano threefolds", Jpn. J. Math, 13(1), pp.109~185 (2018)[DOI]
- S. Lee, "Geometry of moduli spaces of rational curves on Fano varieties", Ph.D., pp.2018
- L. Li, "Wonderful compactification of an arrangement of subvarieties", Michigan Math. J, 58(2), pp.535~563 (2009)[DOI]
- Y. G. Prokhorov, "Algebraic geometry and its applications (Yaroslavl, 1992)", pp.159~169 (1994), Aspects Math