4 papers
math.AG2026
On arrangements of plane real quartics with respect to three lines
S. Yu. Orevkov
We complete the classification of mutual arrangements of a smooth real algebraic or real pseudoholomorphic quartic curve and three lines under condition that each oval of the quart…
hep-th2026
Further Bounding the Kreuzer-Skarke Landscape
Nate MacFadden, Stepan Yu. Orevkov, Michael Stepniczka
Batyrev's construction provides a map from fine, regular, star triangulations (FRSTs) of 4D reflexive polytopes to smooth Calabi-Yau threefolds (CYs). We prove that there are at mo…
math.AG2026
On curves of degree 10 with 12 triple points
S. Yu. Orevkov
We construct an irreducible rational curve of degree 10 in which has 12 triple points and a union of three rational quartics with 19 triple points. This gives counter-exampl…
math.AG2025
On germs of mappings
S. Yu. Orevkov
We describe germs of mappings ramified along a germ of irreducible curve whose image is of the form .