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A theory of stacks with twisted fields and resolution of moduli of genus two stable maps
Yi Hu, Jingchen Niu
We construct a smooth algebraic stack of tuples consisting of genus two nodal curves, simple effective divisors away from the nodes, and twisted fields. It provides a desingulariza…
Moduli of Curves of Genus One with Twisted Fields
Yi Hu, Jingchen Niu
We construct a smooth Artin stack parameterizing the stable weighted curves of genus one with twisted fields and prove that it is isomorphic to the blowup stack of the moduli of ge…
Relative Resolution and Its Applications
Yi Hu
We present an introduction to the derived and relative resolutions of the moduli of stable maps. We discuss one application and mention a few problems.
The space of complete quotients
Yi Hu, Yijun Shao
We introduce complete quotients over the projective line and prove that they form smooth projective varieties. The resulting parameter spaces coincide with the varieties constructe…
Genus Two Stable Maps, Local Equations and Modular Resolutions
Yi Hu, Jun Li, Jingchen Niu
We provide a geometric construction of a sequence of modular blowups of the Artin stack parameterizing pre-stable pairs consisting of a genus-two nodal curve and a smooth divisor.…
An Invitation to the Local Structures of Moduli of Genus one stable maps
Yi Hu
This informal note provides some elementary examples to motivate the local structural results of [1] on the moduli space of genus one stable maps to projective space. The hope is t…
Notes on Virtual Fundamental Classes
Yi Hu
The paper has been withdrawn.
Quivers, Invariants and Quotient Correspondence
Yi Hu, Sangjib Kim
This paper studies the geometric and algebraic aspects of the moduli spaces of quivers of fence type. We first provide two quotient presentations of the quiver varieties and interp…
Genus-One Stable Maps, Local Equations, and Vakil-Zinger's desingularization
Yi Hu, Jun Li
We describe an algebro-geometric approach to Vakil-Zinger's desingularization of the main component of the moduli of genus one stable maps to projective space. The new approach pro…
A Compactification of the Space of Algebraic Maps from P^1 to P^n
Yi Hu, Jiayuan Lin, Yijun Shao
We provide a natural smooth projective compactification of the space of algebraic maps from the projective line to the projective space of dimension n by adding a divisor with simp…
Toric Degenerations of GIT Quotients, Chow Quotients, and $\bar{M_{0,n}$
Yi Hu
We show that the moduli space of stable n-pointed rational curves can be flatly degenerated to a projective toric variety. We arrive at this by showing that the Chow quotients of t…
Quotients by Reductive Group, Borel Subgroup, Unipotent Group and Maximal Torus
Yi Hu
Consider an algebraic action of a connected complex reductive algebraic group on a complex polarized projective variety. In this paper, we first introduce the nilpotent quotient, t…
Geometric Invariant Theory and Birational Geometry
Yi Hu
In this paper we will survey some recent developments in the last decade or so on variation of Geometric Invariant Theory and its applications to Birational Geometry such as the we…
Factorization Theorem for Projective Varieties with Finite Quotient Singularities
Yi Hu
In this paper, we prove that any two birational projective varieties with finite quotient singularities can be realized as two geometric GIT quotients of a non-singular projective…
Toric degenerations of weight varieties and applications
Philip Foth, Yi Hu
We show that a weight variety, which is a quotient of a flag variety by the maximal torus, admits a flat degeneration to a toric variety. In particular, we show that the moduli spa…
Stable Configurations of Linear Subspaces and Quotient Coherent Sheaves
Yi Hu
In this paper we provide some stability criteria for systems of linear subspaces of and for systems of quotient coherent sheaves, using, respectively, the Hilbert-Mum…
Topological Aspects of Chow Quotients
Yi Hu
This paper studies the canonical Chow quotient of a smooth projective variety by a reductive algebraic group. The main purpose is to give some topological interpretations and chara…
HyperKähler Manifolds and Birational Transformations
Yi Hu, S. -T. Yau
In this paper we study the birational geometry of HyperKaehler manifolds by combining the method of minimal model program and the traditional approach of symplectic geometry.
Toric morphisms and fibrations of toric Calabi-Yau hypersurfaces
Yi Hu, Chien-Hao Liu, Shing-Tung Yau
Special fibrations of toric varieties have been used by physicists, e.g. the school of Candelas, to construct dual pairs in the study of Het/F-theory duality. Motivated by this, we…
HyperKähler Manifolds and Birational Transformations in dimension 4
Dan Burns, Yi Hu, Tie Luo
We show that any birational map between projective hyperKähler manifolds of dimension 4 is composed of a sequence of simple flops or elementary Mukai transformations under the assu…
Mori Dream Spaces and GIT
Yi Hu, Sean Keel
The main goal of this paper is to study varieties with the best possible Mori theoretic properties (measured by the existence of a certain decomposition of the cone of effective di…
A GIT proof of Włodarczyk's weighted factorization theorem
Yi Hu, Sean Keel
We give a short proof of W{\lodarczyk's theorem that any birational map between smooth projective varieties in characteristic zero is a composition of weighted blowups and blowdown…