Equisingularity classes of birational projections of normal singularities to a plane

Maria Alberich-Carraminana; Jesus Fernandez-Sanchez

Home/Archive/arXiv

arXiv · 0707.1387

Equisingularity classes of birational projections of normal singularities to a plane

Maria Alberich-Carraminana·Jesus Fernandez-Sanchez

View original source ↗Read source document ↗Export metadata ↓

Abstract

Given a birational normal extension S of a two-dimensional local regular ring R, we describe all the equisingularity types of the complete ideals J in R whose blowing-up has some point at which the local ring is analytically isomorphic to S. The problem of classifying the germs of such normal surface singularities was already posed by Spivakovsky (Ann. of Math. 1990). This problem has two parts: discrete and continous. The continous part is to some extent equivalent to the problem of the moduli of plane curve singularities, while the main result of this paper solves completely the discrete part.

Explore related subjects

math.AG math.AC

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Maria Alberich-Carraminana, Jesus Fernandez-Sanchez. 2007-07-10. Equisingularity classes of birational projections of normal singularities to a plane. https://arxiv.org/abs/0707.1387

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Braid and Phantom

Let N be the moduli space of stable rank 2 vector bundles on a smooth projective curve of genus g>1 with fixed odd determinant. With Sebastian Torres, we previously found a semi-orthogonal decomposition of the bounded derived category of N into bounded derived categories of symmetric powers of the curve and, possibly, a phantom block. In this work, we employ the theory of weaving patterns to eliminate the possibility of a phantom, completing the proof of the decomposition conjectured by Narasimhan and, independently, by Belmans, Galkin, and Mukhopadhyay.

math.AG↗

arXiv2026

On the Alexander polynomials of conic-line arrangements

In the present paper we compute Alexander polynomials for certain classes of conic-line arrangements in the complex projective plane which are related to pencils. We prove two general results for curve arrangements coming from Halphen pencils of index $k\geq 2$. Then we apply them to the Hesse arrangement of conics and to some of its degenerations. The results are completed by computations using computer algebra. In particular, we construct conic-line arrangements which are non-reduced pencil-type arrangements and have as roots of their Alexander polynomials roots of unity of order 7. Such roots are not known and are conjectured not to exist in the class of line arrangements.

math.AG↗

arXiv2026

On the Tensor Property of Bernstein-Sato Polynomial

We prove the multiplicative Thom-Sebastiani rule for Bernstein-Sato polynomials, answering the longstanding questions of Budur and Popa. We generalize the result to the tensor of two effective divisors on the product of two arbitrary non-singular complex varieties. This also leads to a multiplicative property related to Igusa's strong monodromy conjecture. Moreover, we propose an extension of our result to Bernstein-Sato polynomials for ideals and prove it for monomial ideals.

math.AG↗