Searcharxiv⌕ Search

arXiv subjects

Quy Thuong Lê

Publications and source records attributed to Quy Thuong Lê.

8 recordsLinked to original sources
arXiv2026

Equivariant motivic integration on special formal schemes

In this article, we construct an equivariant version of motivic integration on special formal schemes that generalizes our previous work for algebraic varieties. Pointing out the existence of an equivariant Néron smoothening for a flat generically smooth special formal scheme, we prove a change of variables formula in this integration. Finally, the article introduces the motivic Milnor fiber of a formal power series. It predicts that this quantity is the right one to define the motivic Milnor fiber of a germ of complex analytic functions.

math.AG↗
arXiv2024

The $p$-adic zeta function of a plane curve singularity

Using toric modifications and some compatibility we compute the local $p$-adic zeta function of a plane curve singularity. Thanks to the compatibility, we can work over the analytic change of variables formula for $p$-adic integrals, hence avoid adapting to the algebraic setting and Denef's formula.

math.AG↗
arXiv2023

Higher Jacobian ideals, contact equivalence and motivic zeta functions

We show basic properties of higher Jacobian matrices and higher Jacobian ideals for functions and apply it to obtain two results concerning singularities of functions. Firstly, we prove that a higher Nash blowup algebra is invariant under contact equivalences, which was recently conjectured by Hussain, Ma, Yau and Zuo. Secondly, we obtain an analogue of a result on motivic nearby cycles by Bussi, Joyce and Meinhardt.

math.AG↗
arXiv2023

Cohomology of contact loci

We construct a spectral sequence converging to the cohomology with compact support of the m-th contact locus of a complex polynomial. The first page is explicitly described in terms of a log resolution and coincides with the first page of McLean's spectral sequence converging to the Floer cohomology of the m-th iterate of the monodromy, when the polynomial has an isolated singularity. Inspired by this connection, we conjecture that if two germs of holomorphic functions are embedded topologically equivalent, then the Milnor fibers of the their tangent cones are homotopy equivalent.

math.AG↗
arXiv2021

Topological zeta functions of complex plane curve singularities

We study topological zeta functions of complex plane curve singularities using toric modifications and further developments. As applications of the research method, we prove that the topological zeta function is a topological invariant for complex plane curve singularities, we give a short and new proof of the monodromy conjecture for plane curves.

math.AG↗
arXiv2021

Geometry of nondegenerate polynomials: Motivic nearby cycles and Cohomology of contact loci

We study polynomials with complex coefficients which are nondegenerate in two senses, one of Kouchnirenko and the other with respect to its Newton polyhedron, through data on contact loci and motivic nearby cycles. Introducing an explicit description of these quantities we can answer in part to questions concerning the motivic nearby cycles of restriction functions and the integral identity conjecture in the context of Newton nondegenerate polynomials. Furthermore, in the nondegeneracy in the sense of Kouchnirenko, we give calculations on cohomology groups of the contact loci.

math.AG↗