toric ideals
Recently Published Documents


TOTAL DOCUMENTS

86
(FIVE YEARS 3)

H-INDEX

11
(FIVE YEARS 0)

Author(s):  
Ken-ichi Hayase ◽  
Takayuki Hibi ◽  
Koyo Katsuno ◽  
Kazuki Shibata

2021 ◽  
Vol 574 ◽  
pp. 409-433
Author(s):  
Giuseppe Favacchio ◽  
Johannes Hofscheier ◽  
Graham Keiper ◽  
Adam Van Tuyl
Keyword(s):  

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Michał Lasoń

AbstractIn 1980 White conjectured that every element of the toric ideal of a matroid is generated by quadratic binomials corresponding to symmetric exchanges. We prove White’s conjecture for high degrees with respect to the rank. This extends our result (Lasoń and Michałek in Adv Math 259:1–12, 2014) confirming White’s conjecture ‘up to saturation’. Furthermore, we study degrees of Gröbner bases and Betti tables of the toric ideals of matroids of a fixed rank.


Author(s):  
JiSun Huh ◽  
Sangwook Kim ◽  
Boram Park
Keyword(s):  

2020 ◽  
Vol 3 (4) ◽  
pp. 831-837
Author(s):  
Akihiro Higashitani ◽  
Hidefumi Ohsugi
Keyword(s):  

2020 ◽  
Vol 148 (11) ◽  
pp. 4665-4677
Author(s):  
Giuseppe Favacchio ◽  
Graham Keiper ◽  
Adam Van Tuyl
Keyword(s):  

2020 ◽  
Vol 31 (5-6) ◽  
pp. 461-482
Author(s):  
Michele Rossi ◽  
Lea Terracini

Abstract We present two algorithms determining all the complete and simplicial fans admitting a fixed non-degenerate set of vectors V as generators of their 1-skeleton. The interplay of the two algorithms allows us to discerning if the associated toric varieties admit a projective embedding, in principle for any values of dimension and Picard number. The first algorithm is slower than the second one, but it computes all complete and simplicial fans supported by V and lead us to formulate a topological-combinatoric conjecture about the definition of a fan. On the other hand, we adapt the Sturmfels’ arguments on the Gröbner fan of toric ideals to our complete case; we give a characterization of the Gröbner region and show an explicit correspondence between Gröbner cones and chambers of the secondary fan. A homogenization procedure of the toric ideal associated to V allows us to employing GFAN and related software in producing our second algorithm. The latter turns out to be much faster than the former, although it can compute only the projective fans supported by V. We provide examples and a list of open problems. In particular we give examples of rationally parametrized families of $$\mathbb {Q}$$ Q -factorial complete toric varieties behaving in opposite way with respect to the dimensional jump of the nef cone over a special fibre.


2020 ◽  
Vol 15 (7) ◽  
pp. 1609-1617
Author(s):  
Hussein S. Mohammed Hussein ◽  
Abdulrahman H. Majeed

Sign in / Sign up

Export Citation Format

Share Document