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Journals and Conferences
We show that the arithmetically Cohen–Macaulay (ACM) curves of degree 4 and genus 0 in P form an irreducible subset of the Hilbert scheme. Using this, we show that the singular locus of the corresponding component of the Hilbert scheme has dimension greater than 6. Moreover, we describe the structures of all ACM curves of Hilb(P).
We show that any smooth Q-normal lattice polytope P of dimension n and degree d is a strict Cayley polytope if n ≥ 2d+ 1. This gives a sharp answer, for this class of polytopes, to a question raised by V. V. Batyrev and B. Nill.
This issue of the Journal of Symbolic Computation collects selected papers on work presented at, or related to, MEGA 2009 held in Barcelona (Spain) from June 15 to June 19, 2009. MEGA is the acronym for ‘‘Effective Methods in Algebraic Geometry’’ and its equivalent in Italian, French, Spanish, German, Russian, etc. This is a series of biennial conferences… (More)
We continue the development of methods for enumerating nodal curves on smooth complex surfaces, stressing the range of validity. We illustrate the new methods in three important examples. First, for up to eight nodes, we confirm Göttsche’s conjecture about plane curves of low degree. Second, we justify Vainsencher’s enumeration of irreducible six-nodal… (More)
The following theorem is proved: The n-th Veronese embedding of P' is the one and only immersion /: X -»P^ where X is a smooth, irreducible r-fold and /n+r\ N=1 j -1. such that the n-th osculating space at every point x of X is all of P .̂ It is also conjectured and verified in some cases-that a smooth, irreducible r-fold X is isomorphic to P*̂ if the… (More)