Tilting bundles on toric Fano fourfolds

Nathan Prabhu-Naik

doi:10.1016/j.jalgebra.2016.09.007

Tilting bundles on toric Fano fourfolds

Nathan Prabhu-Naik

Department of Mathematical Sciences

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

9 Citations (SciVal)

Abstract

This paper constructs tilting bundles obtained from full strong exceptional collections of line bundles on all smooth 4-dimensional toric Fano varieties. The tilting bundles lead to a large class of explicit Calabi–Yau-5 algebras, obtained as the corresponding rolled-up helix algebra. A database of the full strong exceptional collections can be found in the package QuiversToricVarieties for the computer algebra system Macaulay2.

Original language	English
Pages (from-to)	348-398
Number of pages	51
Journal	Journal of Algebra
Volume	471
DOIs	https://doi.org/10.1016/j.jalgebra.2016.09.007
Publication status	Published - 1 Feb 2017

Keywords

Derived category
Quiver algebra
Tilting theory
Toric geometry

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2016.09.007

Cite this

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title = "Tilting bundles on toric Fano fourfolds",

abstract = "This paper constructs tilting bundles obtained from full strong exceptional collections of line bundles on all smooth 4-dimensional toric Fano varieties. The tilting bundles lead to a large class of explicit Calabi–Yau-5 algebras, obtained as the corresponding rolled-up helix algebra. A database of the full strong exceptional collections can be found in the package QuiversToricVarieties for the computer algebra system Macaulay2.",

keywords = "Derived category, Quiver algebra, Tilting theory, Toric geometry",

author = "Nathan Prabhu-Naik",

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AB - This paper constructs tilting bundles obtained from full strong exceptional collections of line bundles on all smooth 4-dimensional toric Fano varieties. The tilting bundles lead to a large class of explicit Calabi–Yau-5 algebras, obtained as the corresponding rolled-up helix algebra. A database of the full strong exceptional collections can be found in the package QuiversToricVarieties for the computer algebra system Macaulay2.

KW - Derived category

KW - Quiver algebra

KW - Tilting theory

KW - Toric geometry

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JO - Journal of Algebra

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ER -

Tilting bundles on toric Fano fourfolds

Abstract

Keywords

ASJC Scopus subject areas

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