Imperial College London
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Professor Richard Thomas FRS

Faculty of Natural Sciences, Department of Mathematics

Royal Society Research Professor (Pure Mathematics)
 
 
 
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Contact

 

richard.thomas Website

 
 
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Location

 

659Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@inbook{Pandharipande:2014:10.1017/CBO9781107279544.007,
author = {Pandharipande, R and Thomas, RP},
booktitle = {Moduli Spaces},
doi = {10.1017/CBO9781107279544.007},
pages = {282--333},
publisher = {Cambridge University Press},
title = {13/2 ways of counting curves},
url = {http://dx.doi.org/10.1017/CBO9781107279544.007},
year = {2014}
}
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RIS format (EndNote, RefMan)

TY  - CHAP
AB  - In the past 20 years, compactifications of the families of curves inalgebraic varieties X have been studied via stable maps, Hilbert schemes,stable pairs, unramified maps, and stable quotients. Each path leads to adifferent enumeration of curves. A common thread is the use of a 2-termdeformation/obstruction theory to define a virtual fundamental class. Therichest geometry occurs when X is a nonsingular projective variety of dimension3.  We survey here the 13/2 principal ways to count curves with special attentionto the 3-fold case. The different theories are linked by a web of conjecturalrelationships which we highlight. Our goal is to provide a guide for graduatestudents looking for an elementary route into the subject.
AU  - Pandharipande,R
AU  - Thomas,RP
DO  - 10.1017/CBO9781107279544.007
EP  - 333
PB  - Cambridge University Press
PY  - 2014///
SN  - 9781107279544
SP  - 282
TI  - 13/2 ways of counting curves
T1  - Moduli Spaces
UR  - http://dx.doi.org/10.1017/CBO9781107279544.007
UR  - http://arxiv.org/abs/1111.1552v2
ER  -
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