Geometric properties of the double-point divisor

Author:
Bo Ilic

Journal:
Trans. Amer. Math. Soc. **350** (1998), 1643-1661

MSC (1991):
Primary 14N05, 14C20, 14J40

DOI:
https://doi.org/10.1090/S0002-9947-98-01928-X

MathSciNet review:
1422899

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Abstract | References | Similar Articles | Additional Information

Abstract: The locus of double points obtained by projecting a variety to a hypersurface in moves in a linear system which is shown to be ample if and only if is not an isomorphic projection of a Roth variety. Such Roth varieties are shown to exist, and some of their geometric properties are determined.

**[ACGH]**E. Arbarello, M. Cornalba, P.A. Griffiths, and J.Harris,*Geometry of algebraic curves*, vol. 1, Springer-Verlag, New York, 1984. MR**86h:14019****[BM]**D. Bayer and D. Mumford,*What can be computed in algebraic geometry?*, Computational algebraic geometry and commutative algebra (Cortona, 1991), Sympos. Math., XXXIV, Cambridge Univ. Press, 1993, pp. 1-48. MR**95d:13032****[Ein]**L.Ein,*The ramification divisor for branched coverings of*, Math. Ann.**261**(1982), 483-485. MR**84c:14009****[EH]**D. Eisenbud and J. Harris,*On varieties of minimal degree (a centennial account)*, Proceedings of the Symposia in Pure Math, vol 46, part 1, A.M.S, 1987, pp. 3-13. MR**89f:14042****[FL]**W. Fulton and R. Lazarsfeld,*Connectivity and its applications in algebraic geometry*, Algebraic geometry (Chicago, IL, 1980), Lecture Notes in Math., vol. 862, Springer-Verlag, New York, 1981, pp. 26-92. MR**83i:14002****[Ha1]**J. Harris,*A bound on the geometric genus of projective varieties*, Ann. Scuola Norm. Sup. Pisa Cl. Sci., Ser. 4**8**(1981), 35-68. MR**82h:14010****[Ha2]**Joe Harris,*Algebraic Geometry-a First Course*, Graduate Texts in Math. Vol. 133, Springer-Verlag, New York, 1992. MR**93j:14001****[Hart]**Robin Hartshorne,*Algebraic Geometry*, Graduate Texts in Math. Vol. 52, Springer-Verlag, New York, 1977. MR**57:3116****[HOV]**K. Hulek, C. Okonek, and A. Van de Ven,*Multiplicity-2 structures on Castelnuovo surfaces*, Ann. Scuola Norm. Sup. Pisa Cl. Sci., Ser. 4**13**(1986), 427-448. MR**88c:14052****[I]**Bo Ilic,*Geometric properties of the double-point divisor*, Thesis, Columbia University, 1995, E-prints: alg-geom/950309.**[Io]**Paltin Ionescu,*Embedded projective varieties of small invariants*, Algebraic Geometry, Bucharest 1982, Lecture Notes in Math., vol. 1056, Springer-Verlag, 1984, pp. 142-186. MR**85m:14024****[Kl]**Steven L. Kleiman,*The enumerative theory of singularities*, Real and Complex Singularities, Oslo 1976, P. Holm (ed.), Sijthoff and Noordhoff, Alphen aan den Rijn, 1977, pp. 297-396. MR**58:27960****[Lar]**M. E. Larsen,*On the topology of complex projective manifolds*, Invent. Math.**19**(1973), 251-260. MR**47:7058****[Mum]**David Mumford,*The Red Book of Varieties and Schemes*, Lecture Notes in Math., vol. 1358, Springer-Verlag, Berlin, 1988. MR**89k:14001****[Ro]**Leonard Roth,*On the projective classification of surfaces*, Proc. London Math. Soc. (2)**42**(1937), 142-170.**[So]**Andrew John Sommese,*Hyperplane sections of projective surfaces. I: The adjunction mapping*, Duke Math. Journal**46**(1979), 377-401. MR**82f:14033****[V]**E. Viehweg,*Vanishing theorems*, Jour. Reine Angew. Math.**335**(1982), 1-8. MR**83m:14011****[Zak]**F. L. Zak,*Tangents and secants of algebraic varieties*, Translations of Math. Monographs vol. 127, American Math. Society, 1993. MR**94i:14053**

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Additional Information

**Bo Ilic**

Affiliation:
Department of Mathematics, Columbia University, New York, New York 10027

Address at time of publication:
Department of Mathematics, University of California, Los Angeles, California 90024

Email:
ilic@math.ucla.edu

DOI:
https://doi.org/10.1090/S0002-9947-98-01928-X

Keywords:
Double-point divisor,
Roth variety,
Castelnuovo variety,
secant variety,
conductor,
projection

Received by editor(s):
July 20, 1996

Article copyright:
© Copyright 1998
American Mathematical Society