Zero-dimensional subschemes of ruled varieties

• Autorzy: Edoardo Ballico , Cristiano Bocci , Claudio Fontanari
• Języki publikacji: EN

Abstrakty

EN

Here we study zero-dimensional subschemes of ruled varieties, mainly Hirzebruch surfaces and rational normal scrolls, by applying the Horace method and the Terracini method

Słowa kluczowe

EN

Ruled varieties; Hirzebruch surfaces; fat points; Horace lemma; Grassmann defective varieties; 14N05

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2004
• Tom: 2
• Numer: 4
• Strony: 538-560

Daty

wydano

2004-08-01

online

2004-08-01

Twórcy

autor

Edoardo Ballico

• University of Trento

autor

Cristiano Bocci

• University of Milano

autor

Claudio Fontanari

• University of Trento

Bibliografia

• [1] B. Adlandsvik: “Joins and higher secant varieties”, Math. Scand., Vol. 62, (1987), pp. 213–222.
• [2] J. Alexander and A. Hirschowitz: “Generic hypersurface singularities”, Proc. Indian Acad. Sci. Math. Sci., Vol. 107, (1997), pp. 139–154.
• [3] J. Alexander and A. Hirschowitz: “Polynomial interpolation in several variables”, J. Algebraic Geometry, Vol. 4, (1995), pp. 201–222.
• [4] J. Alexander and A. Hirschowitz: “An asymptotic vanishing theorem for generic unions of multiple points”, Invent. Math., Vol. 140, (2000), pp. 303–325. http://dx.doi.org/10.1007/s002220000053
• [5] E. Arbarello and M. Cornalba: “Footnotes to a paper of Beniamino Segre”, Math. Ann., Vol. 256, (1981), pp. 341–362. http://dx.doi.org/10.1007/BF01679702
• [6] E. Ballico: “On the symmetric algebra of stable vector bundles on curves”, Quart. J. Math., Vol. 52, (2001), pp. 261–268. http://dx.doi.org/10.1093/qjmath/52.3.261
• [7] M. V. Catalisano, A.V. Geramita and G. Gimigliano: “On the secant varieties to the tangential varieties of a Vernnesean”, Proc. Amer. Math., Vol. 130, (2001), pp. 875–895.
• [8] L. Chiantini and C. Ciliberto: “Weakly defective varieties”, Trans. Amer. Math. Soc., Vol. 354, (2002), pp. 151–178. http://dx.doi.org/10.1090/S0002-9947-01-02810-0
• [9] L. Chiantini and C. Ciliberto: “Threefolds with degrenerate secant variety: on a theorem of G. Scorza”, M. Dekker Lect. Notes, Vol. 217, (2001), pp. 111–124.
• [10] L. Chiantini and C. Ciliberto: “The Grassmannians of secant varieties of curves are not defective”, Indag. Math., Vol. 13, (2002), pp. 23–28. http://dx.doi.org/10.1016/S0019-3577(02)90003-0
• [11] L. Chiantini and C. Ciliberto: In preparation.
• [12] L. Chiantini and M. Coppens: “Grassmannians of secant varieties”, Forum Math., Vol. 13, (2001), pp. 615–628. http://dx.doi.org/10.1515/form.2001.025
• [13] C. Ciliberto and R. Miranda: “Interpolations on curvilinear schemes”, J. Algebra, Vol. 203, (1998), pp. 677–678. http://dx.doi.org/10.1006/jabr.1997.7241
• [14] C. Ciliberto and R. Miranda: “The Segre and Harbourne- Hirschowitz conjectures”, In: Applications of algebraic geometry to coding theory, physics and computation (Eilat 2001), NSTO Sci. Ser. II Math. Phys. Chem., Vol. 36, Kluwer Acad. Publ., Dordrecht, 2001, pp. 37–51.
• [15] C. Ciliberto: ‘Sogni sulle varietà secanti”, Firenze, 18 Aprile, (2002).
• [16] M. Coppens: “The Weierstrass gap sequence of the ordinary ramification points of trigonal coverings of ℙ1; existence of a kind of Weierstrass gap sequence”, J. Pure Appl. Algebra, Vol. 43, (1986), pp. 11–25. http://dx.doi.org/10.1016/0022-4049(86)90002-2
• [17] M. Coppens: Smooth threefolds with G 2,3 -defect, 2003, preprint.
• [18] M. Dale: “Terracini’s lemma and the secant variety of a curve”, Proc. London Math. Soc. (3), Vol. 49, (1984), pp. 329–339.
• [19] C. Dionisi and C. Fontanari: “Grassmann defectivity à la Terracini”, Le Matematiche, Vol. 56, (2001), pp. 245–255.
• [20] C. Fontanari: “Grassmann defective surfaces”, Bollettino U.M.I., Vol. 8(7-B), (2004), pp. 369–379.
• [21] C. Fontanari: “On Waring’s problem for many forms and Grassmann defective varieties”, J. Pure Appl. Algebra, Vol. 74(3), (2002), pp. 243–247. http://dx.doi.org/10.1016/S0022-4049(02)00066-X
• [22] B. Harbourne: “The geometry of rational surfaces and Hilbert functions of points in the plane”, In: Proceedings of the 1984 Vancouver Conference in Algebraic Geometry, Can. Math. Soc. Conf. Proc., Vol. 6, Providence, RI, 1986, pp. 95–111.
• [23] R. Hartshorne and A. Hirschowitz: “Droites en position générale dans l’espace projectif”, In: Algebraic Geometry, Proc., La Rabida 1981, Lect. Notes in Math., Vol. 961, Springer, 1982, pp. 169–189.
• [24] A. Hirschowitz: “La méthode d’Horace pour l’interpolation a plusieurs variables”, Manuscripta Math., Vol. 50, (1985), pp. 337–378. http://dx.doi.org/10.1007/BF01168836
• [25] A. Hirschowitz: “Une conjecture pour la cohomologie des diviseurs sur les surfaces rationelles génériques”, J. Reine Angew. Math., Vol. 397, (1989), pp. 208–213.
• [26] A. Laface: “On linear systems of curves on rational scrolls”, Geom. Dedicata, Vol. 90, (2002), pp. 127–144. http://dx.doi.org/10.1023/A:1014958409472
• [27] F. Palatini: “Sulle superficie algebriche i cui s h (h+1)-seganti non riempiono lo spazio ambiente”, Atti Accad. Torino, Vol. 41, (1906), pp. 634–640.
• [28] F. Palatini: “Sulle varietà algebriche per le quali sono di dimensione minore dell’ordinario senza riempire lo spazio ambiente, una o alcune delle varietà formate da spazi seganti”, Atti. Accad Torino, Vol. 44, (1909), pp. 362–374.
• [29] G. Scorza: “Un problema sui sistemi lineari di curve appartenenti a una superficie algebrica”, Rend. R. Ist. Lombardo, Vol. 2(41), (1908), pp. 813–920.
• [30] G. Scorza: “Determinazione delle varietà a tre dimensioni di S r (r>-7) i cui S 3 tangenti si taglianoa due a due”, Rend. Circ. Mat. Palermo, Vol. 25, (1908), pp. 193–204.
• [31] G. Scorza: “Sulle varietà a quattro dimensioni di S r (r>-9) i cui S 4 tangenti si tagliano a due a due”, Rend. Circ. Mat. Palermo, Vol. 27, (1909), pp. 148–178.
• [32] A. Tannenbaum: “Families of algebraic curves with nodes”, Compositio Math., Vol. 41, (1980), pp. 107–119.
• [33] A. Terracini: “Sulle V K per cui la varietà degli S h (h+1)-seganti ha dimensione minore dell’ordinario”, Rend. Circ. Mat. Palermo, Vol. 31, (1911), pp. 392–396. http://dx.doi.org/10.1007/BF03018812
• [34] A. Terracini: “Sulla rappresentazione delle coppie di forme ternarie mediante somme di potenze di forme lineari”, Ann. di Matem. pura ed appl., Vol. 24(3), (1915), pp. 91–100.
• [35] A. Terracini: “Su due problemi, concernenti la determinazione di alcune classi di superficie, considerati da G. Scorza e. F. Palatini”, Atti Soc. Natur. e Matem. Modena, Vol. 5(6), (1921–1922), pp. 3–16.

Identyfikatory

DOI

10.2478/BF02475962