Comparison of two desingularizations of the moduli space of elliptic stable maps
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
We study the geometry of the moduli space of elliptic stable maps to projective space. The main component of the moduli space of elliptic stable maps is singular. There are two different ways to desingularize this space. One is Vakil-Zinger's desingularization and the other is via the moduli space of logarithmic stable maps. Our main result is a proof of the direct geometric relationship between these two spaces. For degree less than or equal to 3, we prove that the moduli space of logarithmic stable maps can be obtained by blowing up Vakil-Zinger's desingularization.
Abstract
We study the geometry of the moduli space of elliptic stable maps to projective space. The main component of the moduli space of elliptic stable maps is singular. There are two different ways to desingularize this space. One is Vakil-Zinger's desingularization and the other is via the moduli space of logarithmic stable maps. Our main result is a proof of the direct geometric relationship between these two spaces. For degree less than or equal to 3, we prove that the moduli space of logarithmic stable maps can be obtained by blowing up Vakil-Zinger's desingularization.
참고문헌 (9)
- W. Fulton, "Pandharipande, Notes on stable maps and quantum cohomology", Proc. Sympos. Pure Math, 62(2), pp.45~96 (1997), Amer. Math. Soc
- Yi Hu, "Genus-one stable maps, local equations, and Vakil–Zinger’s desingularization", Mathematische Annalen, 348(4), pp.929~963 (2010), Springer Science and Business Media LLC[DOI]
- K. Kato, "Algebraic analysis, geometry, and number theory", pp.191~224 (1989), Johns Hopkins Univ. Press
- B. Kim, "New developments in algebraic geometry, integrable systems and mirror symmetry", pp.167~200 (2010), Math. Soc. Japan
- Alina Marian, "The moduli space of stable quotients", Geometry & Topology, 15(3), pp.1651~1706 (2011), Mathematical Sciences Publishers[DOI]
- David Ishii Smyth, "Modular compactifications of the space of pointed elliptic curves I", Compositio Mathematica, 147(3), pp.877~913 (2011), Wiley[DOI]
- Ravi Vakil, "A natural smooth compactification of the space of elliptic curves in projective space", Electronic Research Announcements of the American Mathematical Society, 13(6), pp.53~59 (2007), American Mathematical Society (AMS)[DOI]
- Ravi Vakil, "A desingularization of the main component of the moduli space of genus-one stable maps into ℙ n", Geometry & Topology, 12(1), pp.1~95 (2008), Mathematical Sciences Publishers[DOI]
- Michael Viscardi, "Alternate compactifications of the moduli space of genus one maps", Manuscripta Mathematica, 139(1-2), pp.201~236 (2012), Springer Science and Business Media LLC[DOI]