Affine toric equivalence relations are effective

@inproceedings{Raicu2009AffineTE,
  title={Affine toric equivalence relations are effective},
  author={Claudiu Raicu},
  year={2009}
}
Any map of schemes defines an equivalence relation , the relation of ``being in the same fiber''. We have shown elsewhere that not every equivalence relation has this form, even if it is assumed to be finite. By contrast, we prove here that every toric equivalence relation on an affine toric variety does come from a morphism and that quotients by finite toric equivalence relations always exist in the affine case. In special cases, this result is a consequence of the vanishing of the first… 
2 Citations
Quotients by finite equivalence relations
This note studies the existence of quotients by finite set theoretic equivalence relations. May 18: Substantial revisions with a new appendix by C. Raicu
Secant varieties to high degree Veronese reembeddings, catalecticant matrices and smoothable Gorenstein schemes
We study the secant varieties of the Veronese varieties and of Veronese reembeddings of a smooth projective variety. We give some conditions, under which these secant varieties are set-theoretically

References

SHOWING 1-10 OF 27 REFERENCES
Construction of Hilbert and Quot Schemes
This is an expository account of Grothendieck's construction of Hilbert and Quot Schemes, following his talk 'Techniques de construction et theoremes d'existence en geometrie algebriques IV : les
Binomial Ideals
We investigate the structure of ideals generated by binomials (polynomials with at most two terms) and the schemes and varieties associated to them. The class of binomial ideals contains many
Quotients by finite equivalence relations
This note studies the existence of quotients by finite set theoretic equivalence relations. May 18: Substantial revisions with a new appendix by C. Raicu
Epimorphisms and Dominions. IV
According to Grothendieck’s definition, which is by now standard in part of the literature, an epimorphism is a map f: A → B such that for any maps g: B → C, h: B → C, if g ≠ h, then gf ≠ hf. In
Introduction to Affine Group Schemes
I The Basic Subject Matter.- 1 Affine Group Schemes.- 1.1 What We Are Talking About.- 1.2 Representable Functors.- 1.3 Natural Maps and Yoneda's Lemma.- 1.4 Hopf Algebras.- 1.5 Translating from
Fundamentals of semigroup theory
1. Introductory ideas 2. Green's equivalences regular semigroups 3. 0-simple semigroups 4. Completely regular semigroups 5. Inverse semigroups 6. Other classes of regular semigroups 7. Free
Editors
  • Computer Science
    Brain Research Bulletin
  • 1986
...
...