• Corpus ID: 238583124

Families of pointed toric varieties and degenerations

@inproceedings{Rocco2021FamiliesOP,
  title={Families of pointed toric varieties and degenerations},
  author={Sandra Di Rocco and Luca Schaffler},
  year={2021}
}
The Losev–Manin moduli space parametrizes pointed chains of projective lines. In this paper we study a possible generalization to families of pointed degenerate toric varieties. Geometric properties of these families, such as flatness and reducedness of the fibers, are explored via a combinatorial characterization. We show that such families are described by a specific type of polytope fibration which generalizes the twisted Cayley sums, originally introduced to characterize elementary extremal… 

Figures and Tables from this paper

References

SHOWING 1-10 OF 23 REFERENCES
Logarithmic stable toric varieties and their moduli
The Chow quotient of a toric variety by a subtorus, as defined by Kapranov-Sturmfels-Zelevinsky, coarsely represents the main component of the moduli space of stable toric varieties with a map to a
Moduli spaces of weighted pointed stable curves
Abstract A weighted pointed curve consists of a nodal curve and a sequence of marked smooth points, each assigned a number between zero and one. A subset of the marked points may coincide if the sum
Universal stacky semistable reduction
Given a log smooth morphism f: X → S of toroidal embeddings, we perform a Raynaud-Gruson type operation on f to make it flat and with reduced fibers. We do this by studying the geometry of the
Complete moduli in the presence of semiabelian group action
I prove the existence, and describe the structure, of moduli space of pairs (P, Θ) consisting of a projective variety P with semiabelian group action and an ample Cartier divisor on it satisfying a
Fiber Fans and Toric Quotients
TLDR
The Toric variety defined by the fan Σ is the normalization of the toric Chow quotient of a closely related affine toric variety by a complementary torus.
Projective Q-factorial toric varieties covered by lines
We give a structural theorem for ℚ-factorial toric varieties covered by lines in ℙN, and compute their dual defect. This yields a characterization of defective ℚ-factorial toric varieties in ℙN. The
Toric stacks II: Intrinsic characterization of toric stacks
The purpose of this paper and its prequel is to introduce and develop a theory of toric stacks which encompasses and extends several notions of toric stacks defined in the literature, as well as
Logarithmic Stable Maps with Torus Actions
of “ Logarithmic Stable Maps with Torus Actions ” by Samouil Molcho, Ph.D., Brown University, May 2014 We study the moduli stacks of logarithmic stable maps when the target variety X is equipped with
Toric stacks I: The theory of stacky fans
The purpose of this paper and its sequel is to introduce and develop a theory of toric stacks which encompasses and extends several notions of toric stacks defined in the literature, as well as
WEAK SEMISTABLE REDUCTION IN CHARACTERISTIC 0
0. INTRODUCTION Regretfully, we work over an algebraically closed eld k of characteristic 0. 0.1. The problem. Roughly speaking, the semistable reduction problem we address here asks for the
...
1
2
3
...