Phylogenetic algebraic geometry

Chapters in this book

1. Frontmatter i
2. Contents vii
3. Characterization of Veronese varieties via projection in Grassmannians 1
4. Birational geometry of defective varieties 13
5. Fano threefolds as hyperplane sections 19
6. Triple points imposing triple divisors and the defective hierarchy 35
7. M15 is rationally connected 51
8. Codimension one decompositions and Chow varieties 67
9. Higher secant varieties of Segre-Veronese varieties 81
10. An appendix to a paper of Catalisano, Geramita, Gimigliano: The Hilbert function of generic sets of 2-fat points in P1 × P1 109
11. The 3-cuspidal quartic and braid monodromy of degree 4 coverings 113
12. On the classification of defective threefolds 131
13. Matching conditions for degenerating plane curves and applications 177
14. Negative curves on very general blow-ups of P2 199
15. Linear congruences and hyperbolic systems of conservation laws 209
16. A note on the very ampleness of complete linear systems on blowings-up of P3 231
17. Phylogenetic algebraic geometry 237
18. Some results on fat points whose support is a complete intersection minus a point 257
19. The (unexpected) importance of knowing α 267
20. Hilbert functions of Gorenstein algebras associated to a pencil of forms 273
21. Varieties of reductions for gln 287
22. Birational geometry of rationally connected manifolds via quasi-lines 317
23. On the discriminant of spanned line bundles 337
24. Multisecant lines to projective varieties 349
25. Cycle map on Hilbert schemes of nodal curves 361
26. Backmatter 379