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Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1
This brief presents a solution to the interpolation problem for arithmetically Cohen-Macaulay (ACM) sets of points in the multiprojective space P^1 x P^1. It collects the various current threads in the literature on this topic with the aim of providing a self-contained, unified introduction while a...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing : Imprint: Springer,
2015.
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| Edición: | 1st ed. 2015. |
| Colección: | SpringerBriefs in Mathematics,
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| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-3-319-24166-1 | ||
| 003 | DE-He213 | ||
| 005 | 20220114170525.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 151125s2015 sz | s |||| 0|eng d | ||
| 020 | |a 9783319241661 |9 978-3-319-24166-1 | ||
| 024 | 7 | |a 10.1007/978-3-319-24166-1 |2 doi | |
| 050 | 4 | |a QA251.3 | |
| 072 | 7 | |a PBF |2 bicssc | |
| 072 | 7 | |a MAT002010 |2 bisacsh | |
| 072 | 7 | |a PBF |2 thema | |
| 082 | 0 | 4 | |a 512.44 |2 23 |
| 100 | 1 | |a Guardo, Elena. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1 |h [electronic resource] / |c by Elena Guardo, Adam Van Tuyl. |
| 250 | |a 1st ed. 2015. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2015. | |
| 300 | |a VIII, 134 p. 25 illus. in color. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a SpringerBriefs in Mathematics, |x 2191-8201 | |
| 505 | 0 | |a Introduction -- The Biprojective Space P^1 x P^1 -- Points in P^1 x P^1 -- Classification of ACM Sets of Points in P^1 x P^1 -- Homological Invariants -- Fat Points in P^1 x P^1 -- Double Points and Their Resolution -- Applications -- References. | |
| 520 | |a This brief presents a solution to the interpolation problem for arithmetically Cohen-Macaulay (ACM) sets of points in the multiprojective space P^1 x P^1. It collects the various current threads in the literature on this topic with the aim of providing a self-contained, unified introduction while also advancing some new ideas. The relevant constructions related to multiprojective spaces are reviewed first, followed by the basic properties of points in P^1 x P^1, the bigraded Hilbert function, and ACM sets of points. The authors then show how, using a combinatorial description of ACM points in P^1 x P^1, the bigraded Hilbert function can be computed and, as a result, solve the interpolation problem. In subsequent chapters, they consider fat points and double points in P^1 x P^1 and demonstrate how to use their results to answer questions and problems of interest in commutative algebra. Throughout the book, chapters end with a brief historical overview, citations of related results, and, where relevant, open questions that may inspire future research. Graduate students and researchers working in algebraic geometry and commutative algebra will find this book to be a valuable contribution to the literature. | ||
| 650 | 0 | |a Commutative algebra. | |
| 650 | 0 | |a Commutative rings. | |
| 650 | 0 | |a Algebraic geometry. | |
| 650 | 0 | |a Projective geometry. | |
| 650 | 1 | 4 | |a Commutative Rings and Algebras. |
| 650 | 2 | 4 | |a Algebraic Geometry. |
| 650 | 2 | 4 | |a Projective Geometry. |
| 700 | 1 | |a Van Tuyl, Adam. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783319241647 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319241654 |
| 830 | 0 | |a SpringerBriefs in Mathematics, |x 2191-8201 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-319-24166-1 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||