Projective Varieties with Unexpected Properties

A Volume in Memory of Giuseppe Veronese. Proceedings of the international conference ‘Varieties with Unexpected Properties’, Siena, Italy, June 8—13, 2004

Ciro Ciliberto, Anthony V. Geramita, Brian Harbourne, Rosa Maria Miró-Roig, Kristian Ranestad, Ciro Ciliberto, Anthony V. Geramita, Brian Harbourne, Rosa Maria Miró-Roig, Kristian Ranestad

• Publisher: De Gruyter
• Year: 2008
• Print ISBN:
  9783110181609
• eBook ISBN:
  9783110199703
• Topic: Mathematics
• Subtopic: Linguistics
• Index: Mathematics

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.

Table of contents

• Frontmatter
• Contents
• Characterization of Veronese varieties via projection in Grassmannians
• Birational geometry of defective varieties
• Fano threefolds as hyperplane sections
• Triple points imposing triple divisors and the defective hierarchy
• M15 is rationally connected
• Codimension one decompositions and Chow varieties
• Higher secant varieties of Segre-Veronese varieties
• An appendix to a paper of Catalisano, Geramita, Gimigliano: The Hilbert function of generic sets of 2-fat points in P1 × P1
• The 3-cuspidal quartic and braid monodromy of degree 4 coverings
• On the classification of defective threefolds
• Matching conditions for degenerating plane curves and applications
• Negative curves on very general blow-ups of P2
• Linear congruences and hyperbolic systems of conservation laws
• A note on the very ampleness of complete linear systems on blowings-up of P3
• Phylogenetic algebraic geometry
• Some results on fat points whose support is a complete intersection minus a point
• The (unexpected) importance of knowing α
• Hilbert functions of Gorenstein algebras associated to a pencil of forms
• Varieties of reductions for gln
• Birational geometry of rationally connected manifolds via quasi-lines
• On the discriminant of spanned line bundles
• Multisecant lines to projective varieties
• Cycle map on Hilbert schemes of nodal curves
• Backmatter