The representation type of rational normal scrolls

被引：24

作者：

Miró-Roig R.M. ^{[1
]}

机构：

[1] Department d'Algebra i Geometria, Facultat de Matemàtiques, University of Barcelona, 08007 Barcelona

来源：

Rendiconti del Circolo Matematico di Palermo | 2013年 / 62卷 / 1期

关键词：

Arithmetic Cohen-Macaulay sheaves; Representation type; Scroll; Ulrich bundles;

D O I：

10.1007/s12215-013-0113-y

中图分类号：

学科分类号：

摘要：

The goal of this paper is to demonstrate that all non-singular rational normal scrolls S(a0,..., ak) ⊆ ℙN, (unless ℙk+1 = S(0,..., 0, 1), the rational normal curve S(a) in ℙa, the quadric surface S(1, 1) in ℙ3 and the cubic scroll S(1,2) in ℙ4 support families of arbitrarily large rank and dimension of simple Ulrich (and hence indecomposable ACM) vector bundles. Therefore, they are all of wild representation type unless ℙk+1 S(a), S(1,1) and S(1,2) which are of finite representation type. © 2013 Springer-Verlag Italia.

引用

页码：153 / 164

页数：11

共 16 条

[1]

Arbarello E., Cornalba M., Griffiths P.A., Harris J., Geometry of algebraic curves, Grundlehren der Mathematischen Wissenschaften, 267, (1985)

[2]

Buchweitz R., Greuel G., Schreyer F.O., Cohen-Macaulay modules on hypersurface singularities, II, Invent. Math., 88, 1, pp. 165-182, (1987)

[3]

Casanellas M., Hartshorne R., Stable Ulrich bundles

[4]

Casanellas M., Hartshorne R., Gorenstein Biliaison and ACM sheaves, J. Algebra, 278, pp. 314-341, (2004)

[5]

Casanellas M., Hartshorne R., ACM bundles on cubic surfaces, J. Eur. Math. Soc., 13, pp. 709-731, (2011)

[6]

Costa L., Miro-Roig R.M., Pons-Llopis J., The representation type of Segre varieties, Adv. Math., 230, pp. 1995-2013, (2012)

[7]

Drozd Y., Greuel G.M., Tame and wild projective curves and classification of vector bundles, J. Algebra, 246, pp. 1-54, (2001)

[8]

Eisenbud D., Schreyer F., Weyman J., Resultants and Chow forms via exterior syzygies, J. Amer. Math. Soc., 16, pp. 537-579, (2003)

[9]

Eisenbud D., Herzog J., The classification of homogeneous Cohen-Macaulay rings of finite representation type, Math. Ann., 280, 2, pp. 347-352, (1988)

[10]

Hartshorne R., Connectedness of the Hilbert scheme, Publications Mathmatiques De L'iHS, 29, pp. 5-48, (1966)

← 1 2 →