Kalkül der abzählenden Geometrie

Schubert, Hermann

doi:10.1007/978-3-642-67228-6

Cited by 91 publications

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“…specified flex lines. In the 1870's, Schubert [15] computed the characteristic numbers of cuspidal plane cubics, and in the 1980's, a lot of work was devoted to the verification of his results, cf. Sacchiero [14], Kleiman-Speiser [8], Miret-Xambó [12], and Aluffi [1].…”

Section: Introductionmentioning

confidence: 99%

Characteristic numbers of rational curves with cusp or prescribed triple contact

Kock¹

2003

MATH. SCAND.

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This note pursues the techniques of [Graber-Kock-Pandharipande] to give concise solutions to the characteristic number problem of rational curves in P 2 or P 1 × P 1 with a cusp or a prescribed triple contact. The classes of such loci are computed in terms of modified psi classes, diagonal classes, and certain codimension-2 boundary classes. Via topological recursions the generating functions for the numbers can then be expressed in terms of the usual characteristic number potentials.

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Section: Introductionmentioning

confidence: 99%

Characteristic numbers of rational curves with cusp or prescribed triple contact

Kock¹

2003

MATH. SCAND.

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“…In 1874 Schubert published a celebrated treatise on Enumerative Geometry [16] which dealt with finding the number of points, lines, planes, etc., satisfying certain geometric conditions. These were important problems in Schubert's time.…”

Section: Two Lines Intersect Four Given Linesmentioning

confidence: 99%

Reconstructing a 3D Line from a Single Catadioptric Image

Lanman

Wachs

Taubin

et al. 2006

Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'06)

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“…There exist two quite different descriptions of the cohomology of G m (U m+n ). On the one hand, Chern [2] gave a description of the cohomology ring H*G m (U m+ ") by means of a specific cellular decomposition of the Grassmann manifolds constructed by Ehresmann [3] which, in turn was based on the work of Schubert [15]. By letting n-»oo, one obtains a decomposition of the infinite Grassmannian G m = G m (U co ).…”

Section: Proposition 23 Let X and Y By G-spaces And Let F:x->y Be Amentioning

confidence: 99%

Maps of Stiefel manifolds and a Borsuk–Ulam theorem

Jaworowski

1989

Proceedings of the Edinburgh Mathematical Society

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We are concerned with the following classical version of the Borsuk–Ulam theorem: Let f:Sn→Rk be a map and let Af = {x∈Sn|fx= f(−x)}. Then, if k≦n, Af≠φ. In fact, theorems due to Yang [17] give an estimation of the size of Af in terms of the cohomology index. This classical theorem concerns the antipodal action of the group G=ℤ2 on Sn. It has been generalized and extended in many ways (see a comprehensive expository article by Steinlein [16]). This author ([9, 10)] and Nakaoka [14] proved “continuous” or “parameterized” versions of the theorem. Analogous theorems for actions of the groups G=S1 or S3 have been proved in [11], and [12]; compare also [4, 5, 6].

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Kalkül der abzählenden Geometrie

Cited by 91 publications

References 0 publications

Characteristic numbers of rational curves with cusp or prescribed triple contact

Characteristic numbers of rational curves with cusp or prescribed triple contact

Reconstructing a 3D Line from a Single Catadioptric Image

Maps of Stiefel manifolds and a Borsuk–Ulam theorem

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