Enumerative algebraic geometry via techniques of symplectic topology and analysis of local obstructions
Name
50595301-MIT.pdf
Description
Full printable version
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17.34 MB
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Author(s)
Zinger, Aleksey, 1975-
Advisor(s)
Tomasz S. Mrowka.
Date Issued
2002
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002.
Includes bibliographical references (p. 239-240).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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