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Elizabeth Wulcan
On a representation of the fundamental class of an ideal due to Lejeune-Jalabert
Annales de la faculté des sciences de Toulouse Sér. 6, 25 no. 5 (2016), p. 1051-1078, doi: 10.5802/afst.1522
Article PDF
[1] Andersson (M.) & Wulcan (E.) Residue currents with prescribed annihilator ideals Ann. Sci. École Norm. Sup. 40 no. 6, p. 985-1007 (2007) Numdam | MR 2419855 | Zbl 1143.32003
[2] Angéniol (B.) & Lejeune-Jalabert (M.) Calcul différentiel et classes caractéristiques en géométrie algébriqueTravaux en Cours, 38 Hermann, Paris (1989) Zbl 0749.14008
[3] Bayer (D.) & Sturmfels (B.) Cellular resolutions of monomial modules J. Reine Angew. Math. 502 p. 123-140 (1998) MR 1647559 | Zbl 0909.13011
[4] Bayer (D.) & Peeva (I.) & Sturmfels (B.) Monomial resolutions Math. Res. Lett. 5, no. 1-2, p. 31-46 (1998) MR 1618363 | Zbl 0909.13010
[5] Coleff (N.) & Herrera (M.) Les courants résiduels associés à une forme méromorphe Lect. Notes in Math. 633, Berlin-Heidelberg-New York (1978) Zbl 0371.32007
[6] Demailly (J.-P.)Complex and Differential geometryavailable at http://www-fourier.ujf-grenoble.fr/ demailly/manuscripts/agbook.pdf
[7] Demailly (J.-P.) & Passare (M.) Courants résiduels et classe fondamentale Bull. Sci. Math. 119, no. 1, p. 85-94 (1995) MR 1313858 | Zbl 0851.32013
[8] Eisenbud (D.) The geometry of syzygies. A second course in commutative algebra and algebraic geometry Graduate Texts in Mathematics, 229. Springer-Verlag, New York (2005) MR 2103875 | Zbl 1066.14001
[9] Fulton (W.) Intersection theory. Ergebnisse der Mathematik und ihrer Grenzgebiete Springer-Verlag, Berlin (1984) MR 732620 | Zbl 0885.14002
[10] Griffiths (P.) & Harris (J.) Principles of algebraic geometry Pure and Applied Mathematics. Wiley-Interscience, New York (1978) MR 507725 | Zbl 0836.14001
[11] Lärkäng (R.) A comparison formula for residue currents Preprint, arXiv:1207.1279
[12] Lärkäng (R.) & Wulcan (E.) Computing residue currents of monomial ideals using comparison formulas Bull. Sci. Math. 138, p. 376-392 (2014) MR 3206474 | Zbl 1296.32002
[13] Lärkäng (R.) & Wulcan (E.) Residue currents and fundamental cycles Preprint, arXiv:1505.07289
[14] Lejeune-Jalabert (M.) Remarque sur la classe fondamentale d’un cycle C. R. Acad. Sci. Paris Sér. I Math. 292, no. 17, p. 801-804 (1981) MR 622423 | Zbl 0474.14031
[15] Lejeune-Jalabert (M.) Liaison et résiduAlgebraic geometry (La Rábida, 1981), p. 233-240, Lecture Notes in Math., 961, Springer, Berlin (1982) MR 708336 | Zbl 0539.13013
[16] Miller (E.) & Sturmfels (B.) Combinatorial commutative algebra Graduate Texts in Mathematics 227 Springer-Verlag, New York (2005) MR 2110098 | Zbl 1066.13001
[17] Miller (E.) & Sturmfels (B.) & Yanagawa (K.) Generic and cogeneric monomial ideals, Symbolic computation in algebra, analysis, and geometry (Berkeley, CA, 1998) J. Symbolic Comput. 29 no 4-5, p. 691-708 (2000) MR 1769661 | Zbl 0955.13008
[18] Stevens (J.) Personal communication(2013)
[19] Taylor (J. L.) Several complex variables with connections to algebraic geometry and Lie groups Graduate Studies in Mathematics, 46 American Mathematical Society, Providence, RI (2002) MR 1900941 | Zbl 1002.32001
Elizabeth Wulcan
On a representation of the fundamental class of an ideal due to Lejeune-Jalabert
Annales de la faculté des sciences de Toulouse Sér. 6, 25 no. 5 (2016), p. 1051-1078, doi: 10.5802/afst.1522
Article PDF
Résumé - Abstract
Lejeune-Jalabert showed that the fundamental class of a Cohen-Macaulay ideal $\mathfrak{a}\subset \mathcal{O}_0$ admits a representation as a residue, constructed from a free resolution of $\mathfrak{a}$, of a certain differential form coming from the resolution. We give an explicit description of this differential form in the case where the free resolution is the Scarf resolution of a generic monomial ideal. As a consequence we get a new proof of Lejeune-Jalabert’s result in this case.
Bibliography
[2] Angéniol (B.) & Lejeune-Jalabert (M.) Calcul différentiel et classes caractéristiques en géométrie algébriqueTravaux en Cours, 38 Hermann, Paris (1989) Zbl 0749.14008
[3] Bayer (D.) & Sturmfels (B.) Cellular resolutions of monomial modules J. Reine Angew. Math. 502 p. 123-140 (1998) MR 1647559 | Zbl 0909.13011
[4] Bayer (D.) & Peeva (I.) & Sturmfels (B.) Monomial resolutions Math. Res. Lett. 5, no. 1-2, p. 31-46 (1998) MR 1618363 | Zbl 0909.13010
[5] Coleff (N.) & Herrera (M.) Les courants résiduels associés à une forme méromorphe Lect. Notes in Math. 633, Berlin-Heidelberg-New York (1978) Zbl 0371.32007
[6] Demailly (J.-P.)Complex and Differential geometryavailable at http://www-fourier.ujf-grenoble.fr/ demailly/manuscripts/agbook.pdf
[7] Demailly (J.-P.) & Passare (M.) Courants résiduels et classe fondamentale Bull. Sci. Math. 119, no. 1, p. 85-94 (1995) MR 1313858 | Zbl 0851.32013
[8] Eisenbud (D.) The geometry of syzygies. A second course in commutative algebra and algebraic geometry Graduate Texts in Mathematics, 229. Springer-Verlag, New York (2005) MR 2103875 | Zbl 1066.14001
[9] Fulton (W.) Intersection theory. Ergebnisse der Mathematik und ihrer Grenzgebiete Springer-Verlag, Berlin (1984) MR 732620 | Zbl 0885.14002
[10] Griffiths (P.) & Harris (J.) Principles of algebraic geometry Pure and Applied Mathematics. Wiley-Interscience, New York (1978) MR 507725 | Zbl 0836.14001
[11] Lärkäng (R.) A comparison formula for residue currents Preprint, arXiv:1207.1279
[12] Lärkäng (R.) & Wulcan (E.) Computing residue currents of monomial ideals using comparison formulas Bull. Sci. Math. 138, p. 376-392 (2014) MR 3206474 | Zbl 1296.32002
[13] Lärkäng (R.) & Wulcan (E.) Residue currents and fundamental cycles Preprint, arXiv:1505.07289
[14] Lejeune-Jalabert (M.) Remarque sur la classe fondamentale d’un cycle C. R. Acad. Sci. Paris Sér. I Math. 292, no. 17, p. 801-804 (1981) MR 622423 | Zbl 0474.14031
[15] Lejeune-Jalabert (M.) Liaison et résiduAlgebraic geometry (La Rábida, 1981), p. 233-240, Lecture Notes in Math., 961, Springer, Berlin (1982) MR 708336 | Zbl 0539.13013
[16] Miller (E.) & Sturmfels (B.) Combinatorial commutative algebra Graduate Texts in Mathematics 227 Springer-Verlag, New York (2005) MR 2110098 | Zbl 1066.13001
[17] Miller (E.) & Sturmfels (B.) & Yanagawa (K.) Generic and cogeneric monomial ideals, Symbolic computation in algebra, analysis, and geometry (Berkeley, CA, 1998) J. Symbolic Comput. 29 no 4-5, p. 691-708 (2000) MR 1769661 | Zbl 0955.13008
[18] Stevens (J.) Personal communication(2013)
[19] Taylor (J. L.) Several complex variables with connections to algebraic geometry and Lie groups Graduate Studies in Mathematics, 46 American Mathematical Society, Providence, RI (2002) MR 1900941 | Zbl 1002.32001
