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October, 2020 Representation type of surfaces in $\mathbb{P}^3$
Edoardo BALLICO, Sukmoon HUH
J. Math. Soc. Japan 72(4): 1097-1118 (October, 2020). DOI: 10.2969/jmsj/81178117

Abstract

The goal of this article is to prove that every surface with a regular point in the three-dimensional projective space of degree at least four, is of wild representation type under the condition that either $X$ is integral or $\mathrm{Pic}(X) \cong \langle \cal{O}_X(1) \rangle$; we construct families of arbitrarily large dimension of indecomposable pairwise non-isomorphic ACM vector bundles. On the other hand, we prove that every non-integral ACM scheme of arbitrary dimension at least two, is also very wild in a sense that there exist arbitrarily large dimensional families of pairwise non-isomorphic ACM non-locally free sheaves of rank one.

Funding Statement

The first author is partially supported by GNSAGA of INDAM (Italy) and MIUR PRIN 2015 ‘Geometria delle varietà algebriche’. The second author is supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2018R1C1A6004285 and No. 2016R1A5A1008055).

Citation

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Edoardo BALLICO. Sukmoon HUH. "Representation type of surfaces in $\mathbb{P}^3$." J. Math. Soc. Japan 72 (4) 1097 - 1118, October, 2020. https://doi.org/10.2969/jmsj/81178117

Information

Received: 28 August 2018; Revised: 15 April 2019; Published: October, 2020
First available in Project Euclid: 28 January 2020

MathSciNet: MR4165924
Digital Object Identifier: 10.2969/jmsj/81178117

Subjects:
Primary: 14F05
Secondary: 13C14, 16G60

Rights: Copyright © 2020 Mathematical Society of Japan

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Vol.72 • No. 4 • October, 2020
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