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Pisón-Casares, P.; Vigneron-Tenorio, A.

First syzygies of toric varieties and Diophantine equations in congruence. (English) Zbl 1082.13510

Commun. Algebra 29, No. 4, 1445-1466 (2001).
Summary: We compute the first syzygies of a subclass of lattice ideals by means of some abstract simplicial complexes. This subclass includes the ideals defining toric varieties. A finite check set containing the minimal first syzygy degrees is determined, and a singly-exponential bound for these degrees is explicited. Integer programming techniques are used, precisely the Hilbert bases for Diophantine equations in congruences.

Cited in 1 Review
Cited in 4 Documents

MSC:

13P99 Computational aspects and applications of commutative rings
13D02 Syzygies, resolutions, complexes and commutative rings
68W30 Symbolic computation and algebraic computation
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
11Y50 Computer solution of Diophantine equations
16S36 Ordinary and skew polynomial rings and semigroup rings

Keywords:

first syzygies; toric varieties; integer programming; Diophantine equations; numerical semigroup ring; algorithm

Citations:

Zbl 1042.14024

Software:

GRIN
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References:

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