Projective Varieties with Unexpected Properties
Description
This volume contains refereed papers related to the lectures and talks given at a conference held in Siena (Italy) in June 2004. Also included are research papers that grew out of discussions among the participants and their collaborators. All the papers are research papers, but some of them also contain expository sections which aim to update the state of the art on the classical subject of special projective varieties and their applications and new trends like phylogenetic algebraic geometry.
The topic of secant varieties and the classification of defective varieties is central and ubiquitous in this volume. Besides the intrinsic interest of the subject, it turns out that it is also relevant in other fields of mathematics like expressions of polynomials as sums of powers, polynomial interpolation, rank tensor computations, Bayesian networks, algebraic statistics and number theory.
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Content
2 - Contents [Seite 7]
3 - Characterization of Veronese varieties via projection in Grassmannians [Seite 9]
4 - Birational geometry of defective varieties [Seite 21]
5 - Fano threefolds as hyperplane sections [Seite 27]
6 - Triple points imposing triple divisors and the defective hierarchy [Seite 43]
7 - M15 is rationally connected [Seite 59]
8 - Codimension one decompositions and Chow varieties [Seite 75]
9 - Higher secant varieties of Segre-Veronese varieties [Seite 89]
10 - An appendix to a paper of Catalisano, Geramita, Gimigliano: The Hilbert function of generic sets of 2-fat points in P1 × P1 [Seite 117]
11 - The 3-cuspidal quartic and braid monodromy of degree 4 coverings [Seite 121]
12 - On the classification of defective threefolds [Seite 139]
13 - Matching conditions for degenerating plane curves and applications [Seite 185]
14 - Negative curves on very general blow-ups of P2 [Seite 207]
15 - Linear congruences and hyperbolic systems of conservation laws [Seite 217]
16 - A note on the very ampleness of complete linear systems on blowings-up of P3 [Seite 239]
17 - Phylogenetic algebraic geometry [Seite 245]
18 - Some results on fat points whose support is a complete intersection minus a point [Seite 265]
19 - The (unexpected) importance of knowing a [Seite 275]
20 - Hilbert functions of Gorenstein algebras associated to a pencil of forms [Seite 281]
21 - Varieties of reductions for gln [Seite 295]
22 - Birational geometry of rationally connected manifolds via quasi-lines [Seite 325]
23 - On the discriminant of spanned line bundles [Seite 345]
24 - Multisecant lines to projective varieties [Seite 357]
25 - Cycle map on Hilbert schemes of nodal curves [Seite 369]
26 - Backmatter [Seite 387]
