On intersections with hypersurfaces and normal pseudo-flatness

• Autorzy: Rams, S.
• Języki publikacji: EN

Abstrakty

EN

We study the behaviour of the families of hypersurfaces that are applied in [4] to estimate the Łojasiewicz exponent and the exponent of separation at infinity. We prove that the hypersurfaces for which v((Z . H)^S, c) is minimal are to be smooth along a subset of Z [intersection of sets] S and to meet some algebraic cones along the tangent space to S.

Słowa kluczowe

PL

przestrzeń analityczna; wielokrotność przecinania się

EN

index of contact; multiplicity of intersection; normal pseudo-flatness

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2000
• Tom: Vol. 48, no 3
• Strony: 335--340
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Rams, S.

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland,

Bibliografia

• [1] R. Achilles, M. Manaresi, Multiplicities of a bigraded ring and intersection theory, Math. Ann., 309 (1997) 573-591.
• [2] R. Achilles, P. Tworzewski, T. Winiarski, On improper isolated intersection in complex analytic geometry, Ann. Polon. Math., 51 (1990) 21-36.
• [3] E. Cygan, Intersection theory and separation exponent in complex analytic geometry, Ann. Polon. Math., 69 (1998) 287-299.
• [4] E. Cygan, T. Krasiński, P. Tworzewski, Separation at infinity and Łojasiewicz exponent of polynomial mappings, Invent. Math., 136 (1999) 75-87.
• [5] R. N. Draper, Intersection theory in analytic geometry, Math. Ann., 180 (1969) 175-204.
• [6] R. Gassler, T. Gaffney, Segre numbers and hypersurface singularities, J. Algebraic Geom., 8 (1999) 695-736.
• [7] R. Gassler, Mixed Segre numbers and integral closures of ideals, preprint http://xxx.lanl.gov/form/math.AG, alg-geom/9703018, 1997.
• [8] H. Hironaka, Normal cones in analytic Whitney stratifications, Publ. Math. IHES, 36 (1969) 127-138.
• [9] Kollár, Effective Nullstellensatz for arbitrary -ideals, preprint http:// xxx.lanl.gov/form/math.AG, a1g-geom/9805091, 1998.
• [10] D. B. Massey, L6 cycles and hypersurface singularities, Lecture Notes in Math., 1615, Springer-Verlag, Berlin, Heidelberg 1995.
• [11] S. Rams, Convergence of holomorphic chains, Ann. Polon. Math., 65 (1997) 227-234.
• [12] S. Rams, On the index of contact and multiplicities for bigraded rings, IMUJ preprint 1999/26, http://www.im.uj.edu.pl/im/preprint, 1999.
• [13] P. Tworzewski, Intersection theory in complex analytic geometry, Ann. Polon. Math., 62 (1995) 177-191.
• [14] P. Tworzewski, T. Winiarski, Continuity of intersection of analytic sets, Ann. Polon. Math.. 47 (1983) 387-396.