On some properties of explicit toric degenerations

M. Marchisio; V. Perduca

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 3, page 779-784
  • ISSN: 0392-4033

Abstract

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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.

How to cite

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Marchisio, M., and Perduca, V.. "On some properties of explicit toric degenerations." Bollettino dell'Unione Matematica Italiana 9-B.3 (2006): 779-784. <http://eudml.org/doc/289640>.

@article{Marchisio2006,
abstract = {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.},
author = {Marchisio, M., Perduca, V.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {779-784},
publisher = {Unione Matematica Italiana},
title = {On some properties of explicit toric degenerations},
url = {http://eudml.org/doc/289640},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Marchisio, M.
AU - Perduca, V.
TI - On some properties of explicit toric degenerations
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/10//
PB - Unione Matematica Italiana
VL - 9-B
IS - 3
SP - 779
EP - 784
AB - 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.
LA - eng
UR - http://eudml.org/doc/289640
ER -

References

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  1. ALEXEEV, V., Complete moduli in the presence of semiabelian group action, Ann. Math., 155 (2002), 611-708. Zbl1052.14017
  2. COX, D., 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/ Zbl1038.14021
  3. FULTON, W., Introduction to Toric Varieties, Ann. of Math. Studies, 13, Princeton University Press, (1993). Zbl0813.14039
  4. GRASSI, A. - MARCHISIO, M. - PERDUCA, V., On Some Geometric Properties of Explicit Toric Degenerations, in preparation. Zbl1150.14010
  5. GRAYSON, D. R. - STILLMAN, M. E., Macaulay 2, a software system for research in algebraic geometry, Avalaible at http://www.math.uiuc.edu/Macaulay2/ 
  6. HU, S., 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. MARCHISIO, M. - PERDUCA, V., On Some Properties of Explicit Toric Degenerations, preprint, 2006. Zbl1150.14010
  8. ODA, T., Convex Bodies and Algebraic Geometry, 15, Springer-Verlag, BerlinHeidelberg (1988). Zbl0628.52002
  9. SOTTILE, F., 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. Zbl1051.14059
  10. STRUMFELS, B., Grobner Bases and Convex Polytopes, American Mathematical Society, University Lecture Series, 8, Providence, RI (1996). MR 97b:13034. 

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