The virtual resolutions package for Macaulay2

Ayah Almousa; Juliette Bruce; Michael Loper; Mahrud Sayrafi

doi:10.2140/jsag.2020.10.51

The virtual resolutions package for Macaulay2

Ayah Almousa
, Juliette Bruce
, Michael Loper
, Mahrud Sayrafi

Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

We introduce the VirtualResolutions package for the computer algebra system Macaulay2. This package has tools to construct, display, and study virtual resolutions for products of projective spaces. The package also has tools for generating curves in ℙ¹ × ℙ², providing sources of interesting virtual resolutions.

Original language	English
Pages (from-to)	51-60
Number of pages	10
Journal	Journal of Software for Algebra and Geometry
Volume	10
Issue number	1
DOIs	https://doi.org/10.2140/jsag.2020.10.51
State	Published - 2020

Bibliographical note

Publisher Copyright:
© 2020, Mathematical Sciences Publishers. All rights reserved.

Funding

Work on this article and the associated Macaulay2 package began at the Macaulay2 Workshop at the University of Wisconsin - Madison funded by NSF grant DMS-1812462. Additional progress was made during the Graduate Workshop in Commutative Algebra for Women and Mathematicians of Minority Genders funded by NSF grant DMS-1908799. The final portion of this article and package was written during a Coding Sprint hosted by the Institute for Mathematics and its Applications (IMA), and we are grateful for their hospitality. Almousa was partially supported by the NSF GRFP under Grant No. DGE-1650441. Bruce was partially supported by the NSF GRFP under Grant No. DGE-1256259 and NSF grant DMS-1502553. Loper was partially supported by the NSF RTG grant DMS-1745638. MSC2010: 13D02, 14M25. Keywords: virtual resolution, products of projective spaces, toric varieties, free resolutions. VirtualResolutions version 1.2

Funders	Funder number
National Science Foundation Arctic Social Science Program	1812462, DMS-1812462, DGE-1256259, 14M25, DMS-1908799, DMS-1745638, 13D02, 1256259, 1502553, 1908799, DMS-1502553, MSC2010, 1745638, DGE-1650441

Keywords

free resolutions
products of projective spaces
toric varieties
virtual resolution

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Discrete Mathematics and Combinatorics
Geometry and Topology

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10.2140/jsag.2020.10.51

Cite this

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title = "The virtual resolutions package for Macaulay2",

abstract = "We introduce the VirtualResolutions package for the computer algebra system Macaulay2. This package has tools to construct, display, and study virtual resolutions for products of projective spaces. The package also has tools for generating curves in ℙ1 {\texttimes} ℙ2, providing sources of interesting virtual resolutions.",

keywords = "free resolutions, products of projective spaces, toric varieties, virtual resolution",

author = "Ayah Almousa and Juliette Bruce and Michael Loper and Mahrud Sayrafi",

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AU - Sayrafi, Mahrud

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AB - We introduce the VirtualResolutions package for the computer algebra system Macaulay2. This package has tools to construct, display, and study virtual resolutions for products of projective spaces. The package also has tools for generating curves in ℙ1 × ℙ2, providing sources of interesting virtual resolutions.

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KW - toric varieties

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The virtual resolutions package for Macaulay2

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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