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Showing 1 to 6 of 6 for “"Hilbert Polynomial"”.
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APPROXIMATE GROBNER BASES A BACKWARDS APPROACH
… the Grobner basis of an approximate polynomial system. The Grobner basis of a polynomial system is arguably the most fundamental object of exact computation polynomial algebra, as it answers many of the important questions of commutative algebra, such as ideal membership and …
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Direct Computation of the Degree 4 Gopakumar -Vafa Invariant on a Calabi -Yau 3 -Fold
… 17-dimensional moduli space of stable sheaves of Hilbert polynomial 4n + 1 on P2 to be 192, using tools of algebraic geometry. This Euler characteristic is equal up to sign to the degree 4 BPS (Gopakumar-Vafa) invariant of local P 2, a (noncompact) Calabi-Yau 3-fold. This is a new result verifying …
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Powers of Monomial Ideals
We study monomial ideals in polynomial rings in two variables x, y over a field K. We determine various monomial ideals I such that Ik = (Mn)k where M is the maximal ideal generated by x, y and k is the least such integer. This is related to the well-known notion of Ratliff-Rush closures of an …
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Kaehler Differential Algebras for 0-Dimensional Schemes and Applications
… Kaehler differential algebras and their Hilbert functions for 0-dimensional schemes in P^n. First we give relations between Kaehler differential 1-forms of fat point schemes and another fat point schemes. Then we determine the Hilbert polynomial and give a sharp bound for the regularity …
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Enumerative invariants for local Calabi-Yau threefolds
… In the second part, we compute the Poincar´e polynomial of the moduli space of stable sheaves with Hilbert polynomial 4n + 1 on P2. This is done by classifying all torus fixed points in the moduli space and computing the torus representation of their tangent spaces. The result is also in …
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Splines on polytopal complexes
… the algebra $C^r(\PC)$ of $C^r$ piecewise polynomial functions (splines) over a subdivision by convex polytopes $\PC$ of a domain $\Omega\subset\R^n$. Interest in this algebra arises in a wide variety of contexts, ranging from approximation theory and computer-aided geometric design to …