arXiv subjects

Charles Turo

Publications and source records attributed to Charles Turo.

2 recordsLinked to original sources

arXiv2020

Deformations of Smooth Complete Toric Varieties: Obstructions and the Cup Product

Let $X$ be a complete $\mathbb{Q}$-factorial toric variety. We explicitly describe the space $H^2(X,T_X)$ and the cup product map $H^1(X,T_X)\times H^1(X,T_X)\to H^2(X,T_X)$ in combinatorial terms. Using this, we give an example of a smooth projective toric threefold for which the cup product map does not vanish, showing that in general, smooth complete toric varieties may have obstructed deformations.

math.AG↗

arXiv2015

Unobstructed Stanley-Reisner Degenerations for Dual Quotient Bundles on $G(2,n)$

Let $Q^*$ denote the dual of the quotient bundle on the Grassmannian $G(2,n)$. We prove that the ideal of $Q^*$ in its natural embedding has initial ideal equal to the Stanley-Reisner ideal of a certain unobstructed simplicial complex. Furthermore, we show that the coordinate ring of $Q^*$ has no infinitesimal deformations for $n>5$.

math.AG↗