Combinatorial Algebraic Geometry

1. Front Matter

   Pages i-viii

   PDF

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

    PDF

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.

• abelian varieties
• convexity
• moduli spaces
• hyperelliptic curves
• tropical Jacobians
• space sextics
• combinatorics

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

  Gregory G. Smith

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

  Bernd Sturmfels

Policies and ethics