Quasismooth hypersurfaces of toric varieties |
Michela Artebani |
Universidad de Concepción |
Abstract: |
D. Cox proved that any normal projective toric variety \[X\] is the quotient of an open subset \[\hat X\] of an affine space for the action of an abelian group \[G\] (for example \[\mathbb P^n\] is the quotient of \[\mathbb A^n\backslash\{0\}\] for a \[\mathbb C^*-\] action) [1]. A hypersurface \[Y\] of \[X\] defined as the zero set of a \[G\] -homogeneous polynomial \[f\] is called quasismooth if the singular locus of \[f\] has empty intersection with \[\hat X\] . Quasismooth hypersurfaces are not smooth in general but they inherit the singularities of the ambient space. In this talk I will give a combinatorial characterization of quasismoothness in terms of the Newton polytope of the hypersurface. This is joint work in progress with P. Comparin and R. Guilbot. |
References |
[1] David A. Cox, The homogeneous coordinate ring of a toric variety, J. Algebraic Geom. 4 (1995), no. 1, 17–50. |