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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Linked determinantal loci and limit linear series
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by John Murray and Brian Osserman
Proc. Amer. Math. Soc. 144 (2016), 2399-2410
DOI: https://doi.org/10.1090/proc/12965
Published electronically: November 20, 2015
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Abstract:

We study (a generalization of) the notion of linked determinantal loci recently introduced by the second author, showing that as with classical determinantal loci, they are Cohen-Macaulay whenever they have the expected codimension. We apply this to prove Cohen-Macaulayness and flatness for moduli spaces of limit linear series, and to prove a comparison result between the scheme structures of Eisenbud-Harris limit linear series and the spaces of limit linear series recently constructed by the second author. This comparison result is crucial in order to study the geometry of Brill-Noether loci via degenerations.
References
  • Winfried Bruns and Aldo Conca, Gröbner bases and determinantal ideals, Commutative algebra, singularities and computer algebra (Sinaia, 2002) NATO Sci. Ser. II Math. Phys. Chem., vol. 115, Kluwer Acad. Publ., Dordrecht, 2003, pp. 9–66. MR 2030262
  • Winfried Bruns and Udo Vetter, Determinantal rings, Lecture Notes in Mathematics, vol. 1327, Springer-Verlag, Berlin, 1988. MR 953963, DOI 10.1007/BFb0080378
  • Melody Chan, Alberto López Martin, Nathan Pflueger, and Montserrat Teixidor i Bigas, Genera of Brill-Noether curves and staircase paths in Young tableaux, preprint, 2015.
  • Abel Castorena, Alberto López Martin, and Montserrat Teixidor i Bigas, Invariants of the Brill-Noether curve, preprint, 2014.
  • David Eisenbud and Joe Harris, Limit linear series: basic theory, Invent. Math. 85 (1986), no. 2, 337–371. MR 846932, DOI 10.1007/BF01389094
  • David Eisenbud and Joe Harris, Existence, decomposition, and limits of certain Weierstrass points, Invent. Math. 87 (1987), no. 3, 495–515. MR 874034, DOI 10.1007/BF01389240
  • David Eisenbud and Joe Harris, The Kodaira dimension of the moduli space of curves of genus $\geq 23$, Invent. Math. 90 (1987), no. 2, 359–387. MR 910206, DOI 10.1007/BF01388710
  • David Eisenbud, Commutative algebra, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995. With a view toward algebraic geometry. MR 1322960, DOI 10.1007/978-1-4612-5350-1
  • Alexander Grothendieck and Jean Dieudonné, Éléments de géométrie algébrique: IV. Étude locale des schémas et des morphismes de schémas, seconde partie, Publications mathématiques de l’I.H.É.S., vol. 24, Institut des Hautes Études Scientifiques, 1965.
  • —, Éléments de géométrie algébrique: IV. Étude locale des schémas et des morphismes de schémas, troisième partie, Publications mathématiques de l’I.H.É.S., vol. 28, Institut des Hautes Études Scientifiques, 1966.
  • David Helm and Brian Osserman, Flatness of the linked Grassmannian, Proc. Amer. Math. Soc. 136 (2008), no. 10, 3383–3390. MR 2415019, DOI 10.1090/S0002-9939-08-08959-4
  • Deepak Khosla, Moduli spaces of curves with linear series and the slope conjecture, ProQuest LLC, Ann Arbor, MI, 2005. Thesis (Ph.D.)–Harvard University. MR 2707230
  • Hideyuki Matsumura, Commutative ring theory, Cambridge Studies in Advanced Mathematics, vol. 8, Cambridge University Press, Cambridge, 1986. Translated from the Japanese by M. Reid. MR 879273
  • Brian Osserman, Limit linear series for curves not of compact type, preprint, 2014.
  • —, Limit linear series moduli stacks in higher rank, preprint, 2014.
  • Brian Osserman and Montserrat Teixidor i Bigas, Linked alternating forms and linked symplectic Grassmannians, Int. Math. Res. Not. IMRN 3 (2014), 720–744. MR 3163565, DOI 10.1093/imrn/rns234
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Bibliographic Information
  • John Murray
  • Affiliation: Department of Mathematics, University of California, Davis, One Shields Ave., Davis, California 95616
  • Brian Osserman
  • Affiliation: Department of Mathematics, University of California, Davis, One Shields Ave., Davis, California 95616
  • MR Author ID: 722512
  • Received by editor(s): December 11, 2014
  • Received by editor(s) in revised form: July 13, 2015, and July 30, 2015
  • Published electronically: November 20, 2015
  • Additional Notes: The second author was partially supported by Simons Foundation grant 279151 during the preparation of this work.
  • Communicated by: Lev Borisov
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 2399-2410
  • MSC (2010): Primary 14D06, 14H57, 14M12
  • DOI: https://doi.org/10.1090/proc/12965
  • MathSciNet review: 3477056