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Symmetries of Fano varieties
Louis Esser, Lena Ji, Joaquín Moraga
We study Fano varieties endowed with a faithful action of a symmetric group, as well as analogous results for Calabi--Yau varieties, and log terminal singularities. We show the exi…
Log canonical pairs with conjecturally minimal volume
Louis Esser, Burt Totaro
We construct log canonical pairs with a nonzero reduced divisor and ample that have the smallest known volume. We conjecture that our examples have the smallest…
Minimal log discrepancies of hypersurface mirrors
Louis Esser
For certain quasismooth Calabi-Yau hypersurfaces in weighted projective space, the Berglund-Hübsch-Krawitz (BHK) mirror symmetry construction gives a concrete description of the mi…
Calabi-Yau varieties of large index
Louis Esser, Burt Totaro, Chengxi Wang
Call a projective variety Calabi-Yau if its canonical divisor is -linearly equivalent to zero. The smallest positive integer with linearly equivalent to zer…
Optimal sine and sawtooth inequalities
Louis Esser, Terence Tao, Burt Totaro +1
We determine the optimal inequality of the form , in the sense that is maximal. We also solve exactly the analogous problem for th…