| dc.identifier.uri | http://hdl.handle.net/1951/60225 | |
| dc.identifier.uri | http://hdl.handle.net/11401/71492 | |
| dc.description.sponsorship | This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. | en_US |
| dc.format | Monograph | |
| dc.format.medium | Electronic Resource | en_US |
| dc.language.iso | en_US | |
| dc.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dc.type | Dissertation | |
| dcterms.abstract | Enumerative geometry is a rich and fascinating subject that has been studied extensively by algebraic geometers. In our thesis however, we approach this subject using methods from differential topology. The method comprises of two parts. The first part involves computing the Euler class of a vector bundle and evaluating it on the fundamental class of a manifold. This is straightforward. The second part involves perturbing a section and computing its contribution near the boundary. This is usually difficult. We have used this method to compute how many degree $d$ curves are there in $\C\P^2$ that pass through $\frac{d(d+3)}{2} -(\delta + m)$ points having $\delta$ nodes and one singularity of codimension $m$ provided $\delta+m\leq 7$. We also indicate how to extend this approach if $\delta+m$ is greater than $7$. | |
| dcterms.available | 2013-05-24T16:38:15Z | |
| dcterms.available | 2015-04-24T14:47:44Z | |
| dcterms.contributor | Sullivan, Dennis Parnell | en_US |
| dcterms.contributor | Zinger, Aleksey | en_US |
| dcterms.contributor | McDuff, Dusa | en_US |
| dcterms.contributor | Starr, Jason Michael. | en_US |
| dcterms.creator | Mukherjee, Ritwik | |
| dcterms.dateAccepted | 2013-05-24T16:38:15Z | |
| dcterms.dateAccepted | 2015-04-24T14:47:44Z | |
| dcterms.dateSubmitted | 2013-05-24T16:38:15Z | |
| dcterms.dateSubmitted | 2015-04-24T14:47:44Z | |
| dcterms.description | Department of Mathematics | en_US |
| dcterms.extent | 102 pg. | en_US |
| dcterms.format | Monograph | |
| dcterms.format | Application/PDF | en_US |
| dcterms.identifier | http://hdl.handle.net/1951/60225 | |
| dcterms.identifier | http://hdl.handle.net/11401/71492 | |
| dcterms.issued | 2011-12-01 | |
| dcterms.language | en_US | |
| dcterms.provenance | Made available in DSpace on 2013-05-24T16:38:15Z (GMT). No. of bitstreams: 1
StonyBrookUniversityETDPageEmbargo_20130517082608_116839.pdf: 41286 bytes, checksum: 425a156df10bbe213bfdf4d175026e82 (MD5)
Previous issue date: 1 | en |
| dcterms.provenance | Made available in DSpace on 2015-04-24T14:47:44Z (GMT). No. of bitstreams: 3
StonyBrookUniversityETDPageEmbargo_20130517082608_116839.pdf.jpg: 1934 bytes, checksum: c116f0e1e7be19420106a88253e31f2e (MD5)
StonyBrookUniversityETDPageEmbargo_20130517082608_116839.pdf.txt: 336 bytes, checksum: 84c0f8f99f2b4ae66b3cc3ade09ad2e9 (MD5)
StonyBrookUniversityETDPageEmbargo_20130517082608_116839.pdf: 41286 bytes, checksum: 425a156df10bbe213bfdf4d175026e82 (MD5)
Previous issue date: 1 | en |
| dcterms.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dcterms.subject | bundle, enumerative, Euler, geometry | |
| dcterms.subject | Mathematics | |
| dcterms.title | Enumerative Geometry via Topological Computations | |
| dcterms.type | Dissertation | |
