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Cohomology of union of quadric surfaces in $mathbbCP^3$

Computing the homology class of a curve using Mayer-VietorisSpace of quintics in $mathbbP^3$ that contain intersection of two quadric surfacesCompute the fundamental and homology groups of $S^3 setminus K$, where $K$ is two linked copies of $S^1$ in $mathbb R^3$Arithmetic genus of complete intersection going wrongCompute the homology groups using Mayer-Vietoris sequenceCohomology groups of the Klein bottle from the definition of cellular cohomology.Deformation Retractions of $X=mathbbR^3-x-C_1-C_2$ and Homology GroupsShow $Q_1 cap Q_2 $ is $cong$ to the elliptic curve in $mathbbP^2$.Mayer-Vietoris and homology of $mathbbCP^2$Determine the homomorphism $i_*:H_1(S^3-g(M))to H_1(S^3-g(partial M))$.

3

$begingroup$

It is known that a degree 4 elliptic curve $Esubset mathbbCP^3$ is the complete intersection of two irreducible quadric surfaces $E=Q_1 cap Q_2.$ Can one compute the (co)homology groups (over $mathbbQ$ coefficients) of the union of these quadric surfaces $H^*(Q_1 cup Q_2)?$
E.g. by looking at the Mayer–Vietoris sequence, one can get that $H^0=mathbbQ,H^1=0,H^4=mathbbQ^2,$ but two results
$$H^2=mathbbQ^6, H^3=mathbbQ$$ and $$H^2=mathbbQ^5, H^3=0$$
both fit in it (at least algebraically). Is there a way to find out which one is correct?

algebraic-geometry algebraic-topology homology-cohomology quadrics

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asked Mar 22 at 14:40

Filip92Filip92

1678

$endgroup$

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3

$begingroup$

It is known that a degree 4 elliptic curve $Esubset mathbbCP^3$ is the complete intersection of two irreducible quadric surfaces $E=Q_1 cap Q_2.$ Can one compute the (co)homology groups (over $mathbbQ$ coefficients) of the union of these quadric surfaces $H^*(Q_1 cup Q_2)?$
E.g. by looking at the Mayer–Vietoris sequence, one can get that $H^0=mathbbQ,H^1=0,H^4=mathbbQ^2,$ but two results
$$H^2=mathbbQ^6, H^3=mathbbQ$$ and $$H^2=mathbbQ^5, H^3=0$$
both fit in it (at least algebraically). Is there a way to find out which one is correct?

algebraic-geometry algebraic-topology homology-cohomology quadrics

share|cite|improve this question

asked Mar 22 at 14:40

Filip92Filip92

1678

$endgroup$

add a comment | 

$begingroup$

It is known that a degree 4 elliptic curve $Esubset mathbbCP^3$ is the complete intersection of two irreducible quadric surfaces $E=Q_1 cap Q_2.$ Can one compute the (co)homology groups (over $mathbbQ$ coefficients) of the union of these quadric surfaces $H^*(Q_1 cup Q_2)?$
E.g. by looking at the Mayer–Vietoris sequence, one can get that $H^0=mathbbQ,H^1=0,H^4=mathbbQ^2,$ but two results
$$H^2=mathbbQ^6, H^3=mathbbQ$$ and $$H^2=mathbbQ^5, H^3=0$$
both fit in it (at least algebraically). Is there a way to find out which one is correct?

algebraic-geometry algebraic-topology homology-cohomology quadrics

share|cite|improve this question

asked Mar 22 at 14:40

Filip92Filip92

1678

$endgroup$

share|cite|improve this question

asked Mar 22 at 14:40

Filip92Filip92

1678

share|cite|improve this question

asked Mar 22 at 14:40

Filip92Filip92

1678

asked Mar 22 at 14:40

Filip92Filip92

1678

asked Mar 22 at 14:40

Filip92Filip92

1678