Counting Ramified Coverings and Intersection Theory on Hurwitz Spaces Ii (local Structure of Hurwitz Spaces and Combinatorial Results)
نویسنده
چکیده
The Hurwitz space is a compactification of the space of rational functions of a given degree. We study the intersection of various strata of this space with its boundary. A study of the cohomology ring of the Hurwitz space then allows us to obtain recurrence relations for certain numbers of ramified coverings of a sphere by a sphere with prescribed ramifications. Generating functions for these numbers belong to a very particular subalgebra of the algebra of power series. 2000 Math. Subj. Class. 05A, 14C, 14D22, 30F.
منابع مشابه
2 00 3 Counting ramified coverings and intersection theory on Hurwitz spaces II ( Local structure of Hurwitz spaces and combinatorial results )
The Hurwitz space is a compactification of the space of rational functions of a given degree. We study the intersection of various strata of this space with its boundary. A study of the cohomology ring of the Hurwitz space then allows us to obtain recurrence relations for certain numbers of ramified coverings of a sphere by a sphere with prescribed ramifications. Generating functions for these ...
متن کاملCounting Ramified Coverings and Intersection Theory on Spaces of Rational Functions I (cohomology of Hurwitz Spaces)
The Hurwitz space is a compactification of the space of rational functions of a given degree. The Lyashko–Looijenga map assigns to a rational function the set of its critical values. It is known that the number of ramified coverings of CP by CP with prescribed ramification points and ramification types is related to the degree of the Lyashko–Looijenga map on various strata of the Hurwitz space....
متن کاملHodge-type integrals on moduli spaces of admissible covers
Hodge integrals are a class of intersection numbers on moduli spaces of curves involving the tautological classes λi, which are the Chern classes of the Hodge bundle E. In recent years Hodge integrals have shown a great amount of interconnections with Gromov-Witten theory and enumerative geometry. The classical Hurwitz numbers, counting the numbers of ramified Covers of a curve with an assigned...
متن کاملEvaluating tautological classes using only Hurwitz numbers
Hurwitz numbers count ramified covers of a Riemann surface with prescribed monodromy. As such, they are purely combinatorial objects. Tautological classes, on the other hand, are distinguished classes in the intersection ring of the moduli spaces of Riemann surfaces of a given genus, and are thus “geometric.” Localization computations in Gromov-Witten theory provide non-obvious relations betwee...
متن کاملComputation of highly ramified coverings
An almost Belyi covering is an algebraic covering of the projective line, such that all ramified points except one simple ramified point lie above a set of 3 points of the projective line. In general, there are 1-dimensional families of these coverings with a fixed ramification pattern. (That is, Hurwitz spaces for these coverings are curves.) In this paper, three almost Belyi coverings of degr...
متن کامل