We study semi-stable degenerations of toric varieties determined by certain partitions of their moment polytopes. We investigate in a particular case their defining equations via a combinatorial analysis. Details, proofs and further examples are contained in the preprint [7] and will be published elsewhere. In a sequel paper [4] we will discuss a geometric interpretation.
Nella presente nota si studiano delle degenerazioni semi-stabili di varietà toriche determinate da certe partizioni dei loro politopi associati. In un caso particolare vengono date le loro equazioni attraverso un'analisi combinatorica. I dettagli, le dimostrazioni e ulteriori esempi si trovano nel preprint [7] e verranno pubblicati altrove. In un successivo articolo [4] verrà discussa una interpretazione geometrica.
@article{BUMI_2006_8_9B_3_779_0, author = {M. Marchisio and V. Perduca}, title = {On some properties of explicit toric degenerations}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {9-A}, year = {2006}, pages = {779-784}, zbl = {1150.14010}, mrnumber = {M274126}, language = {en}, url = {http://dml.mathdoc.fr/item/BUMI_2006_8_9B_3_779_0} }
Marchisio, M.; Perduca, V. On some properties of explicit toric degenerations. Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006) pp. 779-784. http://gdmltest.u-ga.fr/item/BUMI_2006_8_9B_3_779_0/
[1] Complete moduli in the presence of semiabelian group action, Ann. Math., 155 (2002), 611-708. | Zbl 1052.14017
,[2] What is a toric variety?, Topics in algebraic geometry and geometric modeling, 203-223, Contemp. Math., 334, Amer. Math. Soc., Providence, RI, (2003); also avalaible at http://www.amherst.edu/dacox/ | Zbl 1038.14021
,[3] 13, Princeton University Press, (1993). | Zbl 0813.14039
, Introduction to Toric Varieties, Ann. of Math. Studies,[4] On Some Geometric Properties of Explicit Toric Degenerations, in preparation. | Zbl 1150.14010
- - ,[5] Macaulay 2, a software system for research in algebraic geometry, Avalaible at http://www.math.uiuc.edu/Macaulay2/
- ,[6] Semistable Degeneration of Toric Varieties and Their Hypersurfaces, Communications in Analysis and Geometry, 14, n. 1 (2006), 59-89; arXiv:math.AG/0110091, (2001), 1-26.
,[7] On Some Properties of Explicit Toric Degenerations, preprint, 2006. | Zbl 1150.14010
- ,[8] 15, Springer-Verlag, BerlinHeidelberg (1988). | Zbl 0628.52002
, Convex Bodies and Algebraic Geometry,[9] Toric ideals, real toric varieties, and the moment map, Topics in algebraic geometry and geometric modeling, 225-240, Contemp. Math., 334, Amer. Math. Soc., Providence, RI, (2003); arXiv:math.AG/0212044. | Zbl 1051.14059
,[10] 8, Providence, RI (1996). MR 97b:13034.
, Grobner Bases and Convex Polytopes, American Mathematical Society, University Lecture Series,