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Birational geometry is a field of algebraic geometry the goal of which is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given by rational functions rather than polynomials; the map may fail to be defined where the rational functions have poles.

10 votes

Crepant resolutions of cDV singularities?

Background. The threefold compound du Val singularities have been introduced by Miles Reid in the 1980s [R1, R2, R3]. Their geometric description is that a general hyperplane section through the singu …
Evgeny Shinder's user avatar
8 votes
0 answers
138 views

Maximally nodal degree 6 Fano threefolds

Let $X$ be a complete intersection of a quadric and a cubic in $\mathbb{P}^5$. In the smooth case it is a so-called Fano threefold of index one and degree six. I would like to consider the case when …
Evgeny Shinder's user avatar