Large lower bounds for the betti numbers of graded modules with low regularity
| Autor: | Adam Boocher, Derrick Wigglesworth |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Hilbert's syzygy theorem
Conjecture Mathematics::Commutative Algebra 13D02 Betti number Applied Mathematics General Mathematics Polynomial ring 010102 general mathematics 05 social sciences Graded ring Codimension Mathematics - Commutative Algebra Commutative Algebra (math.AC) 01 natural sciences Combinatorics Mathematics - Algebraic Geometry 0502 economics and business FOS: Mathematics 0101 mathematics In degree Algebraic Geometry (math.AG) 050203 business & management Mathematics |
| DOI: | 10.48550/arxiv.1903.12503 |
| Popis: | Suppose that $M$ is a finitely-generated graded module of codimension $c\geq 3$ over a polynomial ring and that the regularity of $M$ is at most $2a-2$ where $a\geq 2$ is the minimal degree of a first syzygy of $M$. Then we show that the sum of the betti numbers of $M$ is at least $\beta_0(M)(2^c + 2^{c-1})$. In addition, if $c \geq 9$ then for each $1\leq i\leq \lceil c/2\rceil$, we show $\beta_i(M)\geq 2\beta_0(M){c \choose i}$. Comment: 14 pages, 2 figures |
| Databáze: | OpenAIRE |
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