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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.
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참고문헌 (9)
참고문헌 신청
W. Fulton / 1997 / Pandharipande, Notes on stable maps and quantum cohomology / Proc. Sympos. Pure Math 62(2):45~96
Yi Hu / 2010 / Genus-one stable maps, local equations, and Vakil–Zinger’s desingularization / Mathematische Annalen 348(4):929~963
K. Kato / 1989 / Algebraic analysis, geometry, and number theory / Johns Hopkins Univ. Press :191~224
B. Kim / 2010 / New developments in algebraic geometry, integrable systems and mirror symmetry / Math. Soc. Japan :167~200
Alina Marian / 2011 / The moduli space of stable quotients / Geometry & Topology 15(3):1651~1706
Yi Hu / 2010 / Genus-one stable maps, local equations, and Vakil–Zinger’s desingularization / Mathematische Annalen 348(4):929~963
K. Kato / 1989 / Algebraic analysis, geometry, and number theory / Johns Hopkins Univ. Press :191~224
B. Kim / 2010 / New developments in algebraic geometry, integrable systems and mirror symmetry / Math. Soc. Japan :167~200
Alina Marian / 2011 / The moduli space of stable quotients / Geometry & Topology 15(3):1651~1706
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