Three Flavors of Extremal Betti Tables

Berkesch, Christine; Erman, Daniel; Kummini, Manoj

doi:10.1007/978-1-4614-5292-8_4

Commutative Algebra 2012

DOI: 10.1007/978-1-4614-5292-8_4

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Three Flavors of Extremal Betti Tables

Christine Berkesch

Daniel Erman

Manoj Kummini³

Abstract: Abstract. We discuss extremal Betti tables of resolutions in three different contexts. We begin over the graded polynomial ring, where extremal Betti tables correspond to pure resolutions. We then contrast this behavior with that of extremal Betti tables over regular local rings and over a bigraded ring.

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2016

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Three themes of syzygies

Fløystad

McCullough

Peeva

2016

Bull. Amer. Math. Soc.

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Abstract. We present three exciting themes of syzygies, where major progress has been made recently: Boij-Söderberg theory, Stillman's question, and syzygies over complete intersections.Free resolutions are both central objects and fruitful tools in commutative algebra. They have many applications in algebraic geometry, computational algebra, invariant theory, hyperplane arrangements, mathematical physics, number theory, and other fields. We introduce and motivate free resolutions and their invariants in Sections 1 and 3. The other sections focus on three hot topics, where major progress has been made recently:• Syzygies over complete intersections (see Section 2), • Stillman's question (see Section 4), • Boij-Söderberg theory (see Sections 5 and 6).Of course, there are a number of other interesting aspects of syzygies. The expository papers [MP, PS] contain many open problems and conjectures.

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Three themes of syzygies

Fløystad

McCullough

Peeva

2016

Bull. Amer. Math. Soc.

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show abstract

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Three Flavors of Extremal Betti Tables

Cited by 1 publication

References 22 publications

Three themes of syzygies

Three themes of syzygies

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