Projective Geometry Related to the Singularities of Theta Divisors of Jacobians

C. Ciliberto; E. Sernesi

Bollettino dell'Unione Matematica Italiana (2010)

  • Volume: 3, Issue: 1, page 93-109
  • ISSN: 0392-4041

Abstract

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By studying the higher order focal properties of a family of linear spaces naturally associated to the singular locus of the theta divisor of a non-hyperelliptic jacobian of genus g ≥ 5 , we give a new proof of the classical theorem of Torelli. Related questions and open problems are also discussed.

How to cite

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Ciliberto, C., and Sernesi, E.. "Projective Geometry Related to the Singularities of Theta Divisors of Jacobians." Bollettino dell'Unione Matematica Italiana 3.1 (2010): 93-109. <http://eudml.org/doc/290664>.

@article{Ciliberto2010,
abstract = {By studying the higher order focal properties of a family of linear spaces naturally associated to the singular locus of the theta divisor of a non-hyperelliptic jacobian of genus $g \ge 5$, we give a new proof of the classical theorem of Torelli. Related questions and open problems are also discussed.},
author = {Ciliberto, C., Sernesi, E.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {93-109},
publisher = {Unione Matematica Italiana},
title = {Projective Geometry Related to the Singularities of Theta Divisors of Jacobians},
url = {http://eudml.org/doc/290664},
volume = {3},
year = {2010},
}

TY - JOUR
AU - Ciliberto, C.
AU - Sernesi, E.
TI - Projective Geometry Related to the Singularities of Theta Divisors of Jacobians
JO - Bollettino dell'Unione Matematica Italiana
DA - 2010/2//
PB - Unione Matematica Italiana
VL - 3
IS - 1
SP - 93
EP - 109
AB - By studying the higher order focal properties of a family of linear spaces naturally associated to the singular locus of the theta divisor of a non-hyperelliptic jacobian of genus $g \ge 5$, we give a new proof of the classical theorem of Torelli. Related questions and open problems are also discussed.
LA - eng
UR - http://eudml.org/doc/290664
ER -

References

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  1. ANDREOTTI, A. - MAYER, A., On period relations for abelian integrals on algebraic curves, Ann. Scuola Norm. Sup. Pisa, 21 (3) (1967), 189-238. Zbl0222.14024MR220740
  2. ARBARELLO, E. - CORNALBA, M. - GRIFFITHS, PH. - HARRIS, J., Geometry of algebraic curves, Volume I, Grundlehren der math. Wisensch, 267 (Springer-Verlag, 1984). MR2807457DOI10.1007/978-3-540-69392-5
  3. ARBARELLO, E. - HARRIS, J., Canonical curves and quadrics of rank 4, Compositio Math., 43 (1981), 145-179. Zbl0494.14011MR622446
  4. BAJRAVANI, A., Focal varieties of curves of genus 6 and 8, preprint. Zbl1194.14047MR2639443DOI10.1007/s12215-010-0009-z
  5. CILIBERTO, C. - VAN DER GEER, G., Andreotti-Mayer Loci and the Schottky Problem, Documenta Math., 13 (2008), 453-504. MR2520473
  6. CILIBERTO, C. - SERNESI, E., Singularities of the theta divisor and congruences of planes, J. Algebraic Geom., 1 (1992), 231-250. Zbl0787.14019MR1144438
  7. CILIBERTO, C. - SERNESI, E., Singularities of the Theta Divisor and Families of Secant Spaces to a Canonical Curve, J. Algebra, 171 (1995), 867-893. Zbl0827.14016MR1315925DOI10.1006/jabr.1995.1040
  8. CILIBERTO, C. - SERNESI, E., On the geometry of canonical curves of odd genus, Comm. in Alg., 28 (12) (2000), 5993-6002. Zbl1005.14011MR1808615DOI10.1080/00927870008827200
  9. DARBOUX, G., Sur le contact des courbes et des surfaces, Bull. Soc. math. de France, 4 (2) (1880). Zbl12.0590.01
  10. EISENBUD, D., Linear sections of determinantal varieties, American J. of Math., 110 (1988), 541-575. Zbl0681.14028MR944327DOI10.2307/2374622
  11. GREEN, M., Quadrics of rank four in the ideal of the canonical curve, Invent. Math., 75 (1984), 85-104. Zbl0542.14018MR728141DOI10.1007/BF01403092
  12. ROGORA, E., Varieties with many lines, Manuscripta math., 82 (1994), 207-226. Zbl0812.14038MR1256160DOI10.1007/BF02567698
  13. SEGRE, B., Sulle V n contenenti più di ∞ n - k ⁢ S k , Nota II, Rend. Accad. Naz. Lincei, 5 (8) (1948), 275-280. MR36042
  14. SEGRE, C., Sui fochi di 2° ordine dei sistemi infiniti di piani, e sulle curve iperspaziali con una doppia infinità di piani plurisecanti. Atti R. Accad. Lincei, 30 (5) (1921), 67-71. Zbl48.0849.02

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