The enumeration of simultaneous higher-order contacts between plane curves

作者: Susan Jane Colley , Gary Kennedy

DOI:

关键词:

摘要: Using the Semple bundle construction, we derive an intersection-theoretic formula for number of simultaneous contacts specified orders between members a generic family degree $d$ plane curves and finitely many fixed curves. The counted by occur at nonsingular points both

参考文章(13)
Paolo Aluffi, The enumerative geometry of plane cubics Mathematische Annalen. ,vol. 289, pp. 543- 572 ,(1991) , 10.1007/BF01446588
Steven L. Kleiman, Robert Speiser, Enumerative geometry of nodal plane cubics Algebraic Geometry Sundance 1986. pp. 156- 196 ,(1988) , 10.1007/BFB0082914
Steven L. Kleiman, The transversality of a general translate Compositio Mathematica. ,vol. 28, pp. 287- 297 ,(1974)
Joel Roberts, Robert Speiser, Enumerative geometry of triangles, II Communications in Algebra. ,vol. 14, pp. 155- 191 ,(1984) , 10.1080/00927878608823302
Geir Ellingsrud, Stein Arild Str�mme, On the homology of the Hilbert scheme of points in the plane Inventiones Mathematicae. ,vol. 87, pp. 343- 352 ,(1987) , 10.1007/BF01389419
Paolo Aluffi, Two characteristic numbers for smooth plane curves of any degree Transactions of the American Mathematical Society. ,vol. 329, pp. 73- 96 ,(1992) , 10.1090/S0002-9947-1992-1041042-5
Geir Ellingsrud, Stein Arild Str�mme, On a cell decomposition of the Hilbert scheme of points in the plane Inventiones Mathematicae. ,vol. 91, pp. 365- 370 ,(1988) , 10.1007/BF01389372
Israel Vainsencher, Counting divisors with prescribed singularities Transactions of the American Mathematical Society. ,vol. 267, pp. 399- 422 ,(1981) , 10.1090/S0002-9947-1981-0626480-7
J. G. Semple, Some Investigations in the Geometry of Curve and Surface Elements Proceedings of the London Mathematical Society. ,vol. s3-4, pp. 24- 49 ,(1954) , 10.1112/PLMS/S3-4.1.24