X. Liao

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20112022

most citedChern Classes Of Logarithmic Vector Fields For Locally-Homogenous Free Divisors

4 citations · 15 across the 11 of their papers we have counts for

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9 papers · 1 filter

math.AG2018★ 1 cited

An approach to Lagrangian specialisation through MacPherson's graph construction

Xia Liao

Let $f : M \to N$ be a holomorphic map between two complex manifolds. Assume $f$ is flat and sans éclatement en codimension 0 (no blowup in codimension 0). We study the theory of La…

math.AG2018

On the explicit calculation of Hirzebruch-Milnor classes of hyperplane arrangements

Xia Liao, Youngho Yoon

The Hirzebruch-Milnor class is given by the difference between the homology Hirzebruch characteristic class and the virtual one. It is known that the Hirzebruch-Milnor class for a…

math.AG2016

K-theoretic defect in Chern class identity for a free divisor

Xia Liao

Let $X$ be a nonsingular variety defined over an algebraically closed field of characteristic $0$ , and $D$ be a free divisor. We study the motivic Chern class of $D$ in the Grothen…

math.AG2014

A cohomological interpretation of derivations on graded algebras

Xia Liao, Mathias Schulze

We trace derivations through Demazure's correspondence between a finitely generated positively graded normal $k$ -algebras $A$ and normal projective $k$ -varieties $X$ equipped with…

math.AG2014★ 3 cited

Quasihomogeneous free divisors with only normal crossings in codimension one

Xia Liao, Mathias Schulze

We prove that any divisor as in the title must be normal crossing.

math.AG2012★ 2 cited

Chern Classes of Logarithmic Derivations for Free Divisors with Jacobian Ideal of Linear Type

Xia Liao

Let $X$ be a nonsingular variety defined over an algebraically closed field of characteristic $0$ , and $D$ be a free divisor with Jacobian ideal of linear type. We compute the Cher…

math.AG2012★ 4 cited

Chern Classes Of Logarithmic Vector Fields For Locally-Homogenous Free Divisors

Xia Liao

Let $X$ be a nonsingular complex projective variety and $D$ a locally quasi-homogeneous free divisor in $X$ . In this paper we study a numerical relation between the Chern class of…

math.AG2012★ 2 cited

Chern Classes of Logarithmic Vector Fields

Xia Liao

Let $X$ be a nonsingular complex variety and $D$ a reduced effective divisor in $X$ . In this paper we study the conditions under which the formula $c_{SM}(1_U)=c(\textup{Der}_X(-\l…

math.AG2011★ 2 cited

Stable Birational Equivalence and Geometric Chevalley-Warning

Xia Liao

We propose a 'geometric Chevalley-Warning' conjecture, that is a motivic extension of the Chevalley-Warning theorem in number theory. It is equivalent to a particular case of a rec…