Purity of the branch locus and Lefschetz theorems
Compositio Mathematica, Tome 96 (1995) no. 2, pp. 173-195.
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     title = {Purity of the branch locus and {Lefschetz} theorems},
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     publisher = {Kluwer Academic Publishers},
     volume = {96},
     number = {2},
     year = {1995},
     mrnumber = {1326711},
     zbl = {0878.13014},
     language = {en},
     url = {http://www.numdam.org/item/CM_1995__96_2_173_0/}
}
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Cutkosky, Steven Dale. Purity of the branch locus and Lefschetz theorems. Compositio Mathematica, Tome 96 (1995) no. 2, pp. 173-195. http://www.numdam.org/item/CM_1995__96_2_173_0/

[AB] M. Auslander and D. Buchsbaum, On ramification theory in noetherian rings, Amer. J. Math. 81 (1959), 749-765. | MR | Zbl

[BE] D. Buchsbaum and D. Eisenbud, Algebra Structures for finite free resolutions, and some structure theorems for ideals of codimension 3, Amer. J. Math. 99 (1977), 447-485. | MR | Zbl

[CS] S.D. Cutkosky and H. Srinivasan, Local fundamental groups of surface singularities in characteristic p, Comment. Math. Helvetici, 68 (1993), 319-332. | MR | Zbl

[F] G. Faltings, Algebraisation of some formal vector bundles, Annals of Mathematics 110 (1979), 501-514. | MR | Zbl

[Fn] H. Flenner, Reine lokale ringe der dimension zwei, Math. Ann. 216 (1975), 253-263. | MR | Zbl

[FH] W. Fulton and J. Hansen, A connectedness theorem for projective varieties, with applications to intersections and singularities of mappings, Annals of Math. 110 (1979), 159-166. | MR | Zbl

[FL] W. Fulton and R. Lazarsfeld, Connectivity and its applications to algebraic geometry, Proc. Midwest Algebraic Geom Conf, 1980, Lecture Notes in Math, vol 862, Springer-Verlag, 1981, 26-92. | MR | Zbl

[GM] M. Goresky and R. Macpherson, Stratified Morse Theory, Springer-Verlag, Berlin (1988). | MR | Zbl

[GR] H. Grauert and R. Remmert, Komplexe Räume, Math. Annalen 136 (1958), 245-318. | MR | Zbl

[EGA] A. Grothendieck, EGA I-IV, Publ. Math. IHES 4,8,11,17,24,28,32.

[SGA1] A. Grothendieck, Revetements étale et groupe fondemental, Lecture notes in Math. 224, Springer-Verlag, Heidelberg (1971). | MR | Zbl

[SGA2] A. Grothendieck, Cohomologie locale des Faisceaux coherents et Theoremes de Lefschetz locaux et globaux, North-Holland, Amsterdam (1968). | MR | Zbl

[H] H.A. Hamm, lokale topologische eigenschaften komplexer räume, Math. Ann. 191 (1971), 235-252. | MR | Zbl

[H1] R. Hartshorne, Ample subvarieties of algebraic varieties, Lecture notes in Math. 156, Springer, Berlin (1970). | MR | Zbl

[HS] R. Hartshorne and R. Speiser, Local cohomological dimension in characteristic p, Ann. of Math. 105 (1977), 45-79. | MR | Zbl

[H] R. Hoobler, Applications of Etale depth to Brauer groups and factorial rings, preprint.

[HH] S. Huckaba and C. Huneke, Rees Algebras of ideals having small analytic deviation, transactions of AMS 339 (1993), 373-402. | MR | Zbl

[L] G. Lyubeznik, Etale cohomological dimension and the topology of algebraic varieties, Annals Math. 137 (1993), 71-128. | MR | Zbl

[M] J.S. Milne, Étale Cohomology, Princeton University press, Princeton, (1980). | MR | Zbl

[N] N. Nagata, On the purity of branch locus in regular local rings, Illinois journal of Math. (1959) 328-333. | Zbl

[O] A. Ogus, Local cohomological dimension of algebraic varieties, Ann. of Math. 98 (1973) 327-365. | MR | Zbl

[PS] C. Peskine, L. Szpiro, Dimension projective finie et cohomologie locale, I.H.E.S. 42 (1973) 327-365. | Numdam

[Ra] M. Raynaud, Theoremes de Lefschetz en cohomologie des faisceaux coherents et en cohomologie etale application au groupe fondamental, Ann. scient, Ec. Norm. Sup. 7 (1974), 29-52. | Numdam | MR | Zbl

[R] T. Room, The geometry of determinental loci, Cambridge University Press, Cambridge, (1938). | JFM | Zbl

[SUV] A. Simmis, B. Ulrich and W. Vasconcelos, Tangent star cones, to appear in Journal of Algebraic Geometry.

[V] W. Vasconcelos, Hilbert functions, analytic spread and Koszul homology, Contemporary Mathematics 159 (1994). | MR | Zbl

[Z] O. Zariski, On the purity of the branch locus of algebraic functions, Proc. Nat. Acad. Sci. USA Vol 44 (1958) 791-796. | MR | Zbl