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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

3 votes
1 answer
424 views

Hilbert's Syzygy Theorem in the bigraded case

I've been recently wondering how to prove the existence of a Hilbert polynomial for finitely generated bigraded modules $M$ over a polynomial ring $R=k[X_0,...,X_n,Y_0,...,Y_m]$ with the usual bigrade …
0 votes
0 answers
237 views

About the multiplicity of intersection in projective space

I found this statement, and I can't get a proof: Given $X\subset \mathbb{P}^{n}$ an irreducible projective set of dimension $d$ and degree $e$, and given $H_{1},...,H_{d}$ hypersurfaces with degrees …