Georg Hein
Preprint series: Institut für Mathematik, Humboldt-Universität
zu Berlin (ISSN 0863-0976), 11pages
MSC 2000
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14C17 Intersection theory, characteristic classes, intersection multiplicities
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14N10 Enumerative problems (combinatorial problems)
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14D22 Fine and coarse moduli spaces
Abstract:
We
attempt to present the intersection theory which is required to understand
the work of Kontsevich and Manin. Finally, we repeat their computations
of intersection numbers in a concrete example. To do so, we study the moduli
stack M of stable maps of degree two from rational curves to P¹. We
show that its Picard group is infinite cyclic. We give an étale
map from M to P² of degree ½. Eventually, we compute an intersection
number which arises in Kontsevich's computation of the number of rational
curves on the quintic threefold.
Keywords:
enumerative geometry, moduli stacks, intersection numbers, quintic threefold
Notes:
This
article will be published in a special volume of the >>Sitzungsberichte
der BMG<< dedicated to H. Kurke on the occasion of his 60th birthday.