arXiv subjects

Luke Cherveny

Publications and source records attributed to Luke Cherveny.

3 recordsLinked to original sources

arXiv2017

The Futaki Invariant of Kähler Blowups with Isolated Zeros via Localization

We present an analytic proof of the relationship between the Calabi-Futaki invariant for a Kähler manifold relative to a holomorphic vector field with a nondegenerate zero and the corresponding invariant of its blowup at that zero, restricting to the case that zeros on the exceptional divisor are isolated. This extends the results of Li and Shi for Kähler surfaces. We also clarify a hypothesis regarding the normal form of the vector field near its zero. An algebro-geometric proof was given by Székelyhidi by reducing the situation to the case of projective manifolds for rational data and using Donaldson-Futaki invariants. Our proof will be an application of degenerate localization.

math.DG↗

arXiv2016

Remarks on Localizing Futaki-Morita Integrals At Isolated Degenerate Zeros

In this note we study the localization of Futaki-Morita integrals at isolated degenerate zeros by giving a streamlined exposition in the spirit of Bott and implement the localization procedure for a holomorphic vector field on $CP^n$ with a maximally degenerate zero, giving an essentially unique formula for the Futaki-Morita integral invariants without using a summation over multiple points. In a coming paper we will apply similar calculations to the Calabi-Futaki invariant of a Kähler blowup.

math.DG↗

arXiv2010

Genus-Zero Mirror Principle For Two Marked Points

We study a generalization of Lian-Liu-Yau's notion of Euler data in genus zero and show that certain sequences of multiplicative equivariant characteristic classes on Kontsevich's stable map moduli with markings induce data satisfying the generalization. In the case of one or two markings, this data is explicitly identified in terms of hypergeometric type classes, constituting a complete extension of Lian-Liu-Yau's mirror principle in genus zero to the case of two marked points and establishing a program for the general case. We give several applications involving the Euler class of obstruction bundles induced by a concavex bundle on $P^n$.

math.AG↗