2026-09-23T08:22:25Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/84022022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Tomasz S. Mrowka.
Zinger, Aleksey, 1975-
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2005-08-23T19:54:37Z
2005-08-23T19:54:37Z
2002
2002
http://hdl.handle.net/1721.1/8402
50595301
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002.
Includes bibliographical references (p. 239-240).
Enumerative geometry of algebraic varieties is a fascinating field of mathematics that dates back to the nineteenth century. We introduce new computational tools into this field that are motivated by recent progress in symplectic topology and its influence on enumerative geometry. The most straightforward applications of the methods developed are to enumeration of rational curves with a cusp of specified nature in projective spaces. A general approach for counting positive-genus curves with a fixed complex structure is also presented. The applications described include enumeration of rational curves with a (3,4)-cusp, genus-two and genus-three curves with a fixed complex structure in the two-dimensional complex projective space, and genus-two curves with a fixed complex structure in the three-dimensional complex projective space. Our constructions may be applicable to problems in symplectic topology as well.
by Aleksey Zinger.
Ph.D.
240 p.
18179663 bytes
18179423 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Enumerative algebraic geometry via techniques of symplectic topology and analysis of local obstructions
Thesis
application/pdf
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