Searcharxiv⌕ Search

arXiv subjects

Sándor J Kovács

Publications and source records attributed to Sándor J Kovács.

23 records · Page 2Linked to original sources
arXiv2012

Du Bois singularities deform

Let $X$ be a variety and $H$ a Cartier divisor on $X$. We prove that if $H$ has Du Bois (or DB) singularities, then $X$ has Du Bois singularities near $H$. As a consequence, if $X \to S$ is a family over a smooth curve $S$ whose special fiber has Du Bois singularities, then the nearby fibers also have Du Bois singularities. We prove this by obtaining an injectivity theorem for certain maps of canonical modules. As a consequence, we also obtain a restriction theorem for certain non-lc ideals.

math.AG↗
arXiv2011

The intuitive definition of Du Bois singularities

It is proved that for projective varieties having Du Bois singularities is equivalent to the condition that the coherent cohomology groups of the structure sheaf coincide with the appropriate Hodge components of the singular cohomology groups.

math.AG↗
arXiv2011

The splitting principle and singularities

The splitting principle states that morphisms in a derived category do not "split" accidentally. This has been successsfully applied in several characterizations of rational, DB, and other singularities. In this article I prove a general statement that implies many of the previous individual statements and improves some of the characterizations in the process.

math.AG↗
arXiv2009

Log canonical singularities are Du Bois

A recurring difficulty in the Minimal Model Program is that while log terminal singularities are quite well behaved (for instance, they are rational), log canonical singularities are much more complicated; they need not even be Cohen-Macaulay. The aim of this paper is to prove that log canonical singularities are Du Bois. The concept of Du Bois singularities, introduced by Steenbrink, is a weakening of rationality. We also prove flatness of the cohomology sheaves of the relative dualizing complex of a projective family with Du Bois fibers. This implies that each connected component of the moduli space of stable log varieties parametrizes either only Cohen-Macaulay or only non-Cohen-Macaulay objects.

math.AG↗