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Combinatorial Algebraic Geometry

Selected Papers From the 2016 Apprenticeship Program

  • Book
  • © 2017

Overview

Editors:
  1. Gregory G. Smith

    1. Department of Mathematics and Statistics, Queen’s University, Kingston, Canada

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    You can also search for this editor in PubMed   Google Scholar

  2. Bernd Sturmfels

    1. Department of Mathematics, University of California, Berkeley, USA

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    You can also search for this editor in PubMed   Google Scholar

  • Bridges the gap between graduate courses and cutting-edge research
  • Covers a wide range of topics in combinatoric algebraic geometry
  • Connects historical sources, computation, explicit examples, and new results

Part of the book series: Fields Institute Communications (FIC, volume 80)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-viii
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  2. Fitness, Apprenticeship, and Polynomials

    • Bernd Sturmfels
    Pages 1-19

  3. From Curves to Tropical Jacobians and Back

    • Barbara Bolognese, Madeline Brandt, Lynn Chua
    Pages 21-45

  4. Tritangent Planes to Space Sextics: The Algebraic and Tropical Stories

    • Corey Harris, Yoav Len
    Pages 47-63

  5. Theta Characteristics of Tropical K 4-Curves

    • Melody Chan, Pakawut Jiradilok
    Pages 65-86

  6. Secants, Bitangents, and Their Congruences

    • Kathlén Kohn, Bernt Ivar Utstøl Nødland, Paolo Tripoli
    Pages 87-112

  7. Equations of \(\overline{M}_{0,n}\)

    • Leonid Monin, Julie Rana
    Pages 113-132

  8. Minkowski Sums and Hadamard Products of Algebraic Varieties

    • Netanel Friedenberg, Alessandro Oneto, Robert L. Williams
    Pages 133-157

  9. Khovanskii Bases of Cox–Nagata Rings and Tropical Geometry

    • Martha Bernal Guillén, Daniel Corey, Maria Donten-Bury, Naoki Fujita, Georg Merz
    Pages 159-179

  10. Equations and Tropicalization of Enriques Surfaces

    • Barbara Bolognese, Corey Harris, Joachim Jelisiejew
    Pages 181-200

  11. Specht Polytopes and Specht Matroids

    • John D. Wiltshire-Gordon, Alexander Woo, Magdalena Zajaczkowska
    Pages 201-228

  12. The Degree of \(\mathop{\mathrm{SO}}\nolimits (n, \mathbb{C})\)

    • Madeline Brandt, Juliette Bruce, Taylor Brysiewicz, Robert Krone, Elina Robeva
    Pages 229-246

  13. Computing Toric Degenerations of Flag Varieties

    • Lara Bossinger, Sara Lamboglia, Kalina Mincheva, Fatemeh Mohammadi
    Pages 247-281

  14. The Multidegree of the Multi-Image Variety

    • Laura Escobar, Allen Knutson
    Pages 283-296

  15. The Convex Hull of Two Circles in \(\mathbb{R}^{3}\)

    • Evan D. Nash, Ata Firat Pir, Frank Sottile, Li Ying
    Pages 297-319

  16. The Hilbert Scheme of 11 Points in \(\mathbb{A}^{3}\) Is Irreducible

    • Theodosios Douvropoulos, Joachim Jelisiejew, Bernt Ivar Utstøl Nødland, Zach Teitler
    Pages 321-352

  17. Towards a Tropical Hodge Bundle

    • Bo Lin, Martin Ulirsch
    Pages 353-368

  18. Cellular Sheaf Cohomology in Polymake

    • Lars Kastner, Kristin Shaw, Anna-Lena Winz
    Pages 369-385

  19. Back Matter

    Pages 387-390
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Keywords

About this book

This volume consolidates selected articles from the 2016 Apprenticeship Program at the Fields Institute, part of the larger program on Combinatorial Algebraic Geometry that ran from July through December of 2016. Written primarily by junior mathematicians, the articles cover a range of topics in combinatorial algebraic geometry including curves, surfaces, Grassmannians, convexity, abelian varieties, and moduli spaces. This book bridges the gap between graduate courses and cutting-edge research by connecting historical sources, computation, explicit examples, and new results.

Editors and Affiliations

  • Department of Mathematics and Statistics, Queen’s University, Kingston, Canada

    Gregory G. Smith

  • Department of Mathematics, University of California, Berkeley, USA

    Bernd Sturmfels

Bibliographic Information

  • Book Title: Combinatorial Algebraic Geometry

  • Book Subtitle: Selected Papers From the 2016 Apprenticeship Program

  • Editors: Gregory G. Smith, Bernd Sturmfels

  • Series Title: Fields Institute Communications

  • DOI: https://doi.org/10.1007/978-1-4939-7486-3

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media LLC 2017

  • Hardcover ISBN: 978-1-4939-7485-6Published: 19 November 2017

  • Softcover ISBN: 978-1-4939-8501-2Published: 23 August 2018

  • eBook ISBN: 978-1-4939-7486-3Published: 17 November 2017

  • Series ISSN: 1069-5265

  • Series E-ISSN: 2194-1564

  • Edition Number: 1

  • Number of Pages: VIII, 390

  • Number of Illustrations: 41 b/w illustrations, 53 illustrations in colour

  • Topics: Algebraic Geometry, Combinatorics

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