81 citations · 371 across the 49 of their papers we have counts for
51 papers
Lines on K3-quartics via triangular sets
Alex Degtyarev, Sławomir Rams
We prove the sharp upper bound of at most lines on a complex K3-surface of degree four with a non-empty singular locus. We also classify the configurations of more than l…
Conics on Barth--Bauer octics
Alex Degtyarev
We analyze the configurations of conics and lines on a special class of Kummer octic surfaces. In particular, we bound the number of conics by and show that there is a unique…
Slope and concordance of links
Alex Degtyarev, Vincent Florens, Ana G. Lecuona
The slope is an isotopy invariant of colored links with a distinguished component, initially introduced by the authors to describe an extra correction term in the computation of th…
Conics in Kummer quartics
Alex Degtyarev
We classify the configurations of lines and conics in smooth Kummer quartics, assuming that all Kummer divisors map to conics. We show that the number of conics on such a quar…
Planes in cubic fourfolds
Alex Degtyarev, Ilia Itenberg, John Christian Ottem
We show that the maximal number of planes in a complex smooth cubic fourfold in is , realized by the Fermat cubic only; the maximal number of real planes in a…
Counting Lines with Vinberg's algorithm
Alex Degtyarev, Sławomir Rams
We combine classical Vinberg's algorithms with the lattice-theoretic/arithmetic approach from arXiv:1706.05734 [math.AG] to give a method of classifying large line configurations o…