CLASSIFICATION OF BETTI DIAGRAMS OF VARIETIES OF ALMOST MINIMAL DEGREE
نویسندگان
چکیده
منابع مشابه
On Varieties of Almost Minimal Degree I : Secant Loci of Rational Normal Scrolls
To provide a geometrical description of the classification theory and the structure theory of varieties of almost minimal degree, that is of non-degenerate irreducible projective varieties whose degree exceeds the codimension by precisely 2, a natural approach is to investigate simple projections of varieties of minimal degree. Let X̃ ⊂ P K be a variety of minimal degree and of codimension at le...
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In this dissertation, we are concerned with decompositions of Betti diagrams over standard graded rings and the information about that ring and its modules that can be recovered from these decompositions. In Chapter 2, we study the structure of modules over short Gorenstein graded rings and determine a necessary condition for a matrix of nonnegative integers to be the Betti diagram of such a mo...
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15 صفحه اولOn Varieties of Almost Minimal Degree Ii: a Rank-depth Formula
We show that the arithmetic depth of the projection Xp of a rational normal scroll X̃ ⊂ P K from a point p ∈ P K \X̃ can be expressed in terms of the rank of the matrix M ′(p), where M ′ is the matrix of linear forms whose 3× 3 minors define the secant variety of X̃.
متن کاملThe Semigroup of Betti Diagrams
The recent proof of the Boij-Söderberg conjectures reveals new structure about Betti diagrams of modules, giving a complete description of the cone of Betti diagrams. We begin to expand on this new structure by investigating the semigroup of Betti diagrams. We prove that this semigroup is finitely generated, and we answer several other fundamental questions about this semigroup.
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ژورنال
عنوان ژورنال: Journal of the Korean Mathematical Society
سال: 2011
ISSN: 0304-9914
DOI: 10.4134/jkms.2011.48.5.1001